diff --git a/esphome/components/bang_bang/bang_bang_climate.cpp b/esphome/components/bang_bang/bang_bang_climate.cpp
index cf527988fe..45d5174390 100644
--- a/esphome/components/bang_bang/bang_bang_climate.cpp
+++ b/esphome/components/bang_bang/bang_bang_climate.cpp
@@ -108,7 +108,7 @@ void BangBangClimate::switch_to_action_(climate::ClimateAction action) {
   }
 
   if (this->prev_trigger_ != nullptr) {
-    this->prev_trigger_->stop();
+    this->prev_trigger_->stop_action();
     this->prev_trigger_ = nullptr;
   }
   Trigger<> *trig;
diff --git a/esphome/components/endstop/endstop_cover.cpp b/esphome/components/endstop/endstop_cover.cpp
index 1c239226c1..8e20cb6a29 100644
--- a/esphome/components/endstop/endstop_cover.cpp
+++ b/esphome/components/endstop/endstop_cover.cpp
@@ -94,7 +94,7 @@ void EndstopCover::dump_config() {
 float EndstopCover::get_setup_priority() const { return setup_priority::DATA; }
 void EndstopCover::stop_prev_trigger_() {
   if (this->prev_command_trigger_ != nullptr) {
-    this->prev_command_trigger_->stop();
+    this->prev_command_trigger_->stop_action();
     this->prev_command_trigger_ = nullptr;
   }
 }
diff --git a/esphome/components/light/base_light_effects.h b/esphome/components/light/base_light_effects.h
index dcef60397d..d6d930e9d4 100644
--- a/esphome/components/light/base_light_effects.h
+++ b/esphome/components/light/base_light_effects.h
@@ -67,9 +67,9 @@ class LambdaLightEffect : public LightEffect {
 class AutomationLightEffect : public LightEffect {
  public:
   AutomationLightEffect(const std::string &name) : LightEffect(name) {}
-  void stop() override { this->trig_->stop(); }
+  void stop() override { this->trig_->stop_action(); }
   void apply() override {
-    if (!this->trig_->is_running()) {
+    if (!this->trig_->is_action_running()) {
       this->trig_->trigger();
     }
   }
diff --git a/esphome/components/script/__init__.py b/esphome/components/script/__init__.py
index 5075bb1f56..eb337d7681 100644
--- a/esphome/components/script/__init__.py
+++ b/esphome/components/script/__init__.py
@@ -2,7 +2,7 @@ import esphome.codegen as cg
 import esphome.config_validation as cv
 from esphome import automation
 from esphome.automation import maybe_simple_id
-from esphome.const import CONF_ID
+from esphome.const import CONF_ID, CONF_MODE
 
 script_ns = cg.esphome_ns.namespace('script')
 Script = script_ns.class_('Script', automation.Trigger.template())
@@ -10,10 +10,47 @@ ScriptExecuteAction = script_ns.class_('ScriptExecuteAction', automation.Action)
 ScriptStopAction = script_ns.class_('ScriptStopAction', automation.Action)
 ScriptWaitAction = script_ns.class_('ScriptWaitAction', automation.Action, cg.Component)
 IsRunningCondition = script_ns.class_('IsRunningCondition', automation.Condition)
+SingleScript = script_ns.class_('SingleScript', Script)
+RestartScript = script_ns.class_('RestartScript', Script)
+QueueingScript = script_ns.class_('QueueingScript', Script, cg.Component)
+ParallelScript = script_ns.class_('ParallelScript', Script)
+
+CONF_SINGLE = 'single'
+CONF_RESTART = 'restart'
+CONF_QUEUE = 'queue'
+CONF_PARALLEL = 'parallel'
+CONF_MAX_RUNS = 'max_runs'
+
+SCRIPT_MODES = {
+    CONF_SINGLE: SingleScript,
+    CONF_RESTART: RestartScript,
+    CONF_QUEUE: QueueingScript,
+    CONF_PARALLEL: ParallelScript,
+}
+
+
+def check_max_runs(value):
+    if CONF_MAX_RUNS not in value:
+        return value
+    if value[CONF_MODE] not in [CONF_QUEUE, CONF_PARALLEL]:
+        raise cv.Invalid("The option 'max_runs' is only valid in 'queue' and 'parallel' mode.",
+                         path=[CONF_MAX_RUNS])
+    return value
+
+
+def assign_declare_id(value):
+    value = value.copy()
+    value[CONF_ID] = cv.declare_id(SCRIPT_MODES[value[CONF_MODE]])(value[CONF_ID])
+    return value
+
 
 CONFIG_SCHEMA = automation.validate_automation({
-    cv.Required(CONF_ID): cv.declare_id(Script),
-})
+    # Don't declare id as cv.declare_id yet, because the ID type
+    # dpeends on the mode. Will be checked later with assign_declare_id
+    cv.Required(CONF_ID): cv.string_strict,
+    cv.Optional(CONF_MODE, default=CONF_SINGLE): cv.one_of(*SCRIPT_MODES, lower=True),
+    cv.Optional(CONF_MAX_RUNS): cv.positive_int,
+}, extra_validators=cv.All(check_max_runs, assign_declare_id))
 
 
 def to_code(config):
@@ -21,6 +58,15 @@ def to_code(config):
     triggers = []
     for conf in config:
         trigger = cg.new_Pvariable(conf[CONF_ID])
+        # Add a human-readable name to the script
+        cg.add(trigger.set_name(conf[CONF_ID].id))
+
+        if CONF_MAX_RUNS in conf:
+            cg.add(trigger.set_max_runs(conf[CONF_MAX_RUNS]))
+
+        if conf[CONF_MODE] == CONF_QUEUE:
+            yield cg.register_component(trigger, conf)
+
         triggers.append((trigger, conf))
 
     for trigger, conf in triggers:
diff --git a/esphome/components/script/script.cpp b/esphome/components/script/script.cpp
new file mode 100644
index 0000000000..f4441b7dcd
--- /dev/null
+++ b/esphome/components/script/script.cpp
@@ -0,0 +1,67 @@
+#include "script.h"
+#include "esphome/core/log.h"
+
+namespace esphome {
+namespace script {
+
+static const char *TAG = "script";
+
+void SingleScript::execute() {
+  if (this->is_action_running()) {
+    ESP_LOGW(TAG, "Script '%s' is already running! (mode: single)", this->name_.c_str());
+    return;
+  }
+
+  this->trigger();
+}
+
+void RestartScript::execute() {
+  if (this->is_action_running()) {
+    ESP_LOGD(TAG, "Script '%s' restarting (mode: restart)", this->name_.c_str());
+    this->stop_action();
+  }
+
+  this->trigger();
+}
+
+void QueueingScript::execute() {
+  if (this->is_action_running()) {
+    // num_runs_ is the number of *queued* instances, so total number of instances is
+    // num_runs_ + 1
+    if (this->max_runs_ != 0 && this->num_runs_ + 1 >= this->max_runs_) {
+      ESP_LOGW(TAG, "Script '%s' maximum number of queued runs exceeded!", this->name_.c_str());
+      return;
+    }
+
+    ESP_LOGD(TAG, "Script '%s' queueing new instance (mode: queue)", this->name_.c_str());
+    this->num_runs_++;
+    return;
+  }
+
+  this->trigger();
+  // Check if the trigger was immediate and we can continue right away.
+  this->loop();
+}
+
+void QueueingScript::stop() {
+  this->num_runs_ = 0;
+  Script::stop();
+}
+
+void QueueingScript::loop() {
+  if (this->num_runs_ != 0 && !this->is_action_running()) {
+    this->num_runs_--;
+    this->trigger();
+  }
+}
+
+void ParallelScript::execute() {
+  if (this->max_runs_ != 0 && this->automation_parent_->num_running() >= this->max_runs_) {
+    ESP_LOGW(TAG, "Script '%s' maximum number of parallel runs exceeded!", this->name_.c_str());
+    return;
+  }
+  this->trigger();
+}
+
+}  // namespace script
+}  // namespace esphome
diff --git a/esphome/components/script/script.h b/esphome/components/script/script.h
index 8495014f00..64db6b80e7 100644
--- a/esphome/components/script/script.h
+++ b/esphome/components/script/script.h
@@ -1,29 +1,86 @@
 #pragma once
 
 #include "esphome/core/automation.h"
+#include "esphome/core/component.h"
 
 namespace esphome {
 namespace script {
 
+/// The abstract base class for all script types.
 class Script : public Trigger<> {
  public:
-  void execute() {
-    bool prev = this->in_stack_;
-    this->in_stack_ = true;
-    this->trigger();
-    this->in_stack_ = prev;
-  }
-  bool script_is_running() { return this->in_stack_ || this->is_running(); }
+  /** Execute a new instance of this script.
+   *
+   * The behavior of this function when a script is already running is defined by the subtypes
+   */
+  virtual void execute() = 0;
+  /// Check if any instance of this script is currently running.
+  virtual bool is_running() { return this->is_action_running(); }
+  /// Stop all instances of this script.
+  virtual void stop() { this->stop_action(); }
+
+  // Internal function to give scripts readable names.
+  void set_name(const std::string &name) { name_ = name; }
 
  protected:
-  bool in_stack_{false};
+  std::string name_;
+};
+
+/** A script type for which only a single instance at a time is allowed.
+ *
+ * If a new instance is executed while the previous one hasn't finished yet,
+ * a warning is printed and the new instance is discarded.
+ */
+class SingleScript : public Script {
+ public:
+  void execute() override;
+};
+
+/** A script type that restarts scripts from the beginning when a new instance is started.
+ *
+ * If a new instance is started but another one is already running, the existing
+ * script is stopped and the new instance starts from the beginning.
+ */
+class RestartScript : public Script {
+ public:
+  void execute() override;
+};
+
+/** A script type that queues new instances that are created.
+ *
+ * Only one instance of the script can be active at a time.
+ */
+class QueueingScript : public Script, public Component {
+ public:
+  void execute() override;
+  void stop() override;
+  void loop() override;
+  void set_max_runs(int max_runs) { max_runs_ = max_runs; }
+
+ protected:
+  int num_runs_ = 0;
+  int max_runs_ = 0;
+};
+
+/** A script type that executes new instances in parallel.
+ *
+ * If a new instance is started while previous ones haven't finished yet,
+ * the new one is exeucted in parallel to the other instances.
+ */
+class ParallelScript : public Script {
+ public:
+  void execute() override;
+  void set_max_runs(int max_runs) { max_runs_ = max_runs; }
+
+ protected:
+  int max_runs_ = 0;
 };
 
 template<typename... Ts> class ScriptExecuteAction : public Action<Ts...> {
  public:
   ScriptExecuteAction(Script *script) : script_(script) {}
 
-  void play(Ts... x) override { this->script_->trigger(); }
+  void play(Ts... x) override { this->script_->execute(); }
 
  protected:
   Script *script_;
@@ -43,7 +100,7 @@ template<typename... Ts> class IsRunningCondition : public Condition<Ts...> {
  public:
   explicit IsRunningCondition(Script *parent) : parent_(parent) {}
 
-  bool check(Ts... x) override { return this->parent_->script_is_running(); }
+  bool check(Ts... x) override { return this->parent_->is_running(); }
 
  protected:
   Script *parent_;
diff --git a/esphome/components/template/cover/template_cover.cpp b/esphome/components/template/cover/template_cover.cpp
index 887f282007..147f76af7d 100644
--- a/esphome/components/template/cover/template_cover.cpp
+++ b/esphome/components/template/cover/template_cover.cpp
@@ -120,7 +120,7 @@ void TemplateCover::set_has_position(bool has_position) { this->has_position_ =
 void TemplateCover::set_has_tilt(bool has_tilt) { this->has_tilt_ = has_tilt; }
 void TemplateCover::stop_prev_trigger_() {
   if (this->prev_command_trigger_ != nullptr) {
-    this->prev_command_trigger_->stop();
+    this->prev_command_trigger_->stop_action();
     this->prev_command_trigger_ = nullptr;
   }
 }
diff --git a/esphome/components/template/switch/template_switch.cpp b/esphome/components/template/switch/template_switch.cpp
index 5868b30996..d9f95e203c 100644
--- a/esphome/components/template/switch/template_switch.cpp
+++ b/esphome/components/template/switch/template_switch.cpp
@@ -19,7 +19,7 @@ void TemplateSwitch::loop() {
 }
 void TemplateSwitch::write_state(bool state) {
   if (this->prev_trigger_ != nullptr) {
-    this->prev_trigger_->stop();
+    this->prev_trigger_->stop_action();
   }
 
   if (state) {
diff --git a/esphome/components/thermostat/thermostat_climate.cpp b/esphome/components/thermostat/thermostat_climate.cpp
index 5d97156e2f..1ffbd3c169 100644
--- a/esphome/components/thermostat/thermostat_climate.cpp
+++ b/esphome/components/thermostat/thermostat_climate.cpp
@@ -223,7 +223,7 @@ void ThermostatClimate::switch_to_action_(climate::ClimateAction action) {
   }
 
   if (this->prev_action_trigger_ != nullptr) {
-    this->prev_action_trigger_->stop();
+    this->prev_action_trigger_->stop_action();
     this->prev_action_trigger_ = nullptr;
   }
   Trigger<> *trig = this->idle_action_trigger_;
@@ -262,7 +262,7 @@ void ThermostatClimate::switch_to_fan_mode_(climate::ClimateFanMode fan_mode) {
     return;
 
   if (this->prev_fan_mode_trigger_ != nullptr) {
-    this->prev_fan_mode_trigger_->stop();
+    this->prev_fan_mode_trigger_->stop_action();
     this->prev_fan_mode_trigger_ = nullptr;
   }
   Trigger<> *trig = this->fan_mode_auto_trigger_;
@@ -313,7 +313,7 @@ void ThermostatClimate::switch_to_mode_(climate::ClimateMode mode) {
     return;
 
   if (this->prev_mode_trigger_ != nullptr) {
-    this->prev_mode_trigger_->stop();
+    this->prev_mode_trigger_->stop_action();
     this->prev_mode_trigger_ = nullptr;
   }
   Trigger<> *trig = this->auto_mode_trigger_;
@@ -355,7 +355,7 @@ void ThermostatClimate::switch_to_swing_mode_(climate::ClimateSwingMode swing_mo
     return;
 
   if (this->prev_swing_mode_trigger_ != nullptr) {
-    this->prev_swing_mode_trigger_->stop();
+    this->prev_swing_mode_trigger_->stop_action();
     this->prev_swing_mode_trigger_ = nullptr;
   }
   Trigger<> *trig = this->swing_mode_off_trigger_;
diff --git a/esphome/components/time_based/time_based_cover.cpp b/esphome/components/time_based/time_based_cover.cpp
index 6d1de144f5..1aa3c2471a 100644
--- a/esphome/components/time_based/time_based_cover.cpp
+++ b/esphome/components/time_based/time_based_cover.cpp
@@ -78,7 +78,7 @@ void TimeBasedCover::control(const CoverCall &call) {
 }
 void TimeBasedCover::stop_prev_trigger_() {
   if (this->prev_command_trigger_ != nullptr) {
-    this->prev_command_trigger_->stop();
+    this->prev_command_trigger_->stop_action();
     this->prev_command_trigger_ = nullptr;
   }
 }
diff --git a/esphome/config_validation.py b/esphome/config_validation.py
index 0649e15f5f..c6ce33dd23 100644
--- a/esphome/config_validation.py
+++ b/esphome/config_validation.py
@@ -812,6 +812,7 @@ def mqtt_qos(value):
 def requires_component(comp):
     """Validate that this option can only be specified when the component `comp` is loaded."""
     def validator(value):
+        # pylint: disable=unsupported-membership-test
         if comp not in CORE.raw_config:
             raise Invalid(f"This option requires component {comp}")
         return value
@@ -1125,7 +1126,7 @@ def typed_schema(schemas, **kwargs):
     def validator(value):
         if not isinstance(value, dict):
             raise Invalid("Value must be dict")
-        if CONF_TYPE not in value:
+        if key not in value:
             raise Invalid("type not specified!")
         value = value.copy()
         key_v = key_validator(value.pop(key))
@@ -1175,6 +1176,7 @@ class OnlyWith(Optional):
 
     @property
     def default(self):
+        # pylint: disable=unsupported-membership-test
         if self._component not in CORE.raw_config:
             return vol.UNDEFINED
         return self._default
diff --git a/esphome/core/automation.h b/esphome/core/automation.h
index 02bd8bb299..6d79480f0f 100644
--- a/esphome/core/automation.h
+++ b/esphome/core/automation.h
@@ -50,18 +50,22 @@ template<typename... Ts> class Automation;
 
 template<typename... Ts> class Trigger {
  public:
+  /// Inform the parent automation that the event has triggered.
   void trigger(Ts... x) {
     if (this->automation_parent_ == nullptr)
       return;
     this->automation_parent_->trigger(x...);
   }
   void set_automation_parent(Automation<Ts...> *automation_parent) { this->automation_parent_ = automation_parent; }
-  void stop() {
+
+  /// Stop any action connected to this trigger.
+  void stop_action() {
     if (this->automation_parent_ == nullptr)
       return;
     this->automation_parent_->stop();
   }
-  bool is_running() {
+  /// Returns true if any action connected to this trigger is running.
+  bool is_action_running() {
     if (this->automation_parent_ == nullptr)
       return false;
     return this->automation_parent_->is_running();
@@ -87,8 +91,18 @@ template<typename... Ts> class Action {
     }
     this->stop_next_();
   }
+  /// Check if this or any of the following actions are currently running.
   virtual bool is_running() { return this->num_running_ > 0 || this->is_running_next_(); }
 
+  /// The total number of actions that are currently running in this plus any of
+  /// the following actions in the chain.
+  int num_running_total() {
+    int total = this->num_running_;
+    if (this->next_ != nullptr)
+      total += this->next_->num_running_total();
+    return total;
+  }
+
  protected:
   friend ActionList<Ts...>;
 
@@ -123,6 +137,8 @@ template<typename... Ts> class Action {
 
   Action<Ts...> *next_ = nullptr;
 
+  /// The number of instances of this sequence in the list of actions
+  /// that is currently being executed.
   int num_running_{0};
 };
 
@@ -151,11 +167,19 @@ template<typename... Ts> class ActionList {
       this->actions_begin_->stop_complex();
   }
   bool empty() const { return this->actions_begin_ == nullptr; }
+
+  /// Check if any action in this action list is currently running.
   bool is_running() {
     if (this->actions_begin_ == nullptr)
       return false;
     return this->actions_begin_->is_running();
   }
+  /// Return the number of actions in this action list that are currently running.
+  int num_running() {
+    if (this->actions_begin_ == nullptr)
+      return false;
+    return this->actions_begin_->num_running_total();
+  }
 
  protected:
   template<int... S> void play_tuple_(const std::tuple<Ts...> &tuple, seq<S...>) { this->play(std::get<S>(tuple)...); }
@@ -177,6 +201,9 @@ template<typename... Ts> class Automation {
 
   bool is_running() { return this->actions_.is_running(); }
 
+  /// Return the number of actions in the action part of this automation that are currently running.
+  int num_running() { return this->actions_.num_running(); }
+
  protected:
   Trigger<Ts...> *trigger_;
   ActionList<Ts...> actions_;