diff --git a/lib/livebook/runtime.ex b/lib/livebook/runtime.ex
index 9f90f2462..34162116e 100644
--- a/lib/livebook/runtime.ex
+++ b/lib/livebook/runtime.ex
@@ -199,4 +199,15 @@ defprotocol Livebook.Runtime do
   """
   @spec duplicate(Runtime.t()) :: {:ok, Runtime.t()} | {:error, String.t()}
   def duplicate(runtime)
+
+  @doc """
+  Returns true if the given runtime is self-contained.
+
+  A standalone runtime always starts fresh and frees all
+  resources when terminated. This may not be the case for
+  for runtimes that connect to an external running system
+  and use it for code evaluation.
+  """
+  @spec standalone?(Runtime.t()) :: boolean()
+  def standalone?(runtime)
 end
diff --git a/lib/livebook/runtime/attached.ex b/lib/livebook/runtime/attached.ex
index 2b65d280b..4d7ebb320 100644
--- a/lib/livebook/runtime/attached.ex
+++ b/lib/livebook/runtime/attached.ex
@@ -71,4 +71,6 @@ defimpl Livebook.Runtime, for: Livebook.Runtime.Attached do
       {:error, :unreachable} -> {:error, "node #{inspect(runtime.node)} is unreachable"}
     end
   end
+
+  def standalone?(_runtime), do: false
 end
diff --git a/lib/livebook/runtime/elixir_standalone.ex b/lib/livebook/runtime/elixir_standalone.ex
index 4958cb196..ec95ee133 100644
--- a/lib/livebook/runtime/elixir_standalone.ex
+++ b/lib/livebook/runtime/elixir_standalone.ex
@@ -97,4 +97,6 @@ defimpl Livebook.Runtime, for: Livebook.Runtime.ElixirStandalone do
   def duplicate(_runtime) do
     Livebook.Runtime.ElixirStandalone.init()
   end
+
+  def standalone?(_runtime), do: true
 end
diff --git a/lib/livebook/runtime/embedded.ex b/lib/livebook/runtime/embedded.ex
index 1ce38edbc..06fed0fa9 100644
--- a/lib/livebook/runtime/embedded.ex
+++ b/lib/livebook/runtime/embedded.ex
@@ -70,4 +70,6 @@ defimpl Livebook.Runtime, for: Livebook.Runtime.Embedded do
   def duplicate(_runtime) do
     Livebook.Runtime.Embedded.init()
   end
+
+  def standalone?(_runtime), do: false
 end
diff --git a/lib/livebook/runtime/mix_standalone.ex b/lib/livebook/runtime/mix_standalone.ex
index 506fdbf2b..d54ebb49f 100644
--- a/lib/livebook/runtime/mix_standalone.ex
+++ b/lib/livebook/runtime/mix_standalone.ex
@@ -150,4 +150,6 @@ defimpl Livebook.Runtime, for: Livebook.Runtime.MixStandalone do
   def duplicate(runtime) do
     Livebook.Runtime.MixStandalone.init(runtime.project_path)
   end
+
+  def standalone?(_runtime), do: true
 end
diff --git a/lib/livebook_web/live/session_live.ex b/lib/livebook_web/live/session_live.ex
index b803cdec5..42f2f59ee 100644
--- a/lib/livebook_web/live/session_live.ex
+++ b/lib/livebook_web/live/session_live.ex
@@ -240,6 +240,7 @@ defmodule LivebookWeb.SessionLive do
                     id: section_view.id,
                     index: index,
                     session_id: @session.id,
+                    runtime: @data_view.runtime,
                     section_view: section_view %>
             <% end %>
             <div style="height: 80vh"></div>
diff --git a/lib/livebook_web/live/session_live/attached_live.ex b/lib/livebook_web/live/session_live/attached_live.ex
index c77cbe852..41675fe68 100644
--- a/lib/livebook_web/live/session_live/attached_live.ex
+++ b/lib/livebook_web/live/session_live/attached_live.ex
@@ -2,12 +2,18 @@ defmodule LivebookWeb.SessionLive.AttachedLive do
   use LivebookWeb, :live_view
 
   alias Livebook.{Session, Runtime, Utils}
+  alias LivebookWeb.SessionLive.RuntimeHelpers
 
   @impl true
   def mount(_params, %{"session" => session, "current_runtime" => current_runtime}, socket) do
+    if connected?(socket) do
+      Phoenix.PubSub.subscribe(Livebook.PubSub, "sessions:#{session.id}")
+    end
+
     {:ok,
      assign(socket,
        session: session,
+       current_runtime: current_runtime,
        error_message: nil,
        data: initial_data(current_runtime)
      )}
@@ -22,6 +28,7 @@ defmodule LivebookWeb.SessionLive.AttachedLive do
           <%= @error_message %>
         </div>
       <% end %>
+      <RuntimeHelpers.default_runtime_note module={Runtime.Attached} />
       <p class="text-gray-700">
         Connect the session to an already running node
         and evaluate code in the context of that node.
@@ -57,13 +64,19 @@ defmodule LivebookWeb.SessionLive.AttachedLive do
         <button class="mt-5 button button-blue"
           type="submit"
           disabled={not data_valid?(@data)}>
-          Connect
+          <%= if(matching_runtime?(@current_runtime, @data), do: "Reconnect", else: "Connect") %>
         </button>
       </.form>
     </div>
     """
   end
 
+  defp matching_runtime?(%Runtime.Attached{} = runtime, data) do
+    initial_data(runtime) == data
+  end
+
+  defp matching_runtime?(_runtime, _data), do: false
+
   @impl true
   def handle_event("validate", %{"data" => data}, socket) do
     {:noreply, assign(socket, data: data)}
@@ -76,7 +89,7 @@ defmodule LivebookWeb.SessionLive.AttachedLive do
     case Runtime.Attached.init(node, cookie) do
       {:ok, runtime} ->
         Session.connect_runtime(socket.assigns.session.pid, runtime)
-        {:noreply, assign(socket, data: data, error_message: nil)}
+        {:noreply, assign(socket, data: initial_data(runtime), error_message: nil)}
 
       {:error, error} ->
         message = runtime_error_to_message(error)
@@ -84,6 +97,13 @@ defmodule LivebookWeb.SessionLive.AttachedLive do
     end
   end
 
+  @impl true
+  def handle_info({:operation, {:set_runtime, _pid, runtime}}, socket) do
+    {:noreply, assign(socket, current_runtime: runtime)}
+  end
+
+  def handle_info(_message, socket), do: {:noreply, socket}
+
   defp initial_data(%Runtime.Attached{node: node, cookie: cookie}) do
     %{
       "name" => Atom.to_string(node),
diff --git a/lib/livebook_web/live/session_live/cell_component.ex b/lib/livebook_web/live/session_live/cell_component.ex
index d37c3a6d0..c8b239de2 100644
--- a/lib/livebook_web/live/session_live/cell_component.ex
+++ b/lib/livebook_web/live/session_live/cell_component.ex
@@ -99,7 +99,7 @@ defmodule LivebookWeb.SessionLive.CellComponent do
 
       <%= if @cell_view.outputs != [] do %>
         <div class="mt-2">
-          <.outputs cell_view={@cell_view} socket={@socket} />
+          <.outputs cell_view={@cell_view} runtime={@runtime} socket={@socket} />
         </div>
       <% end %>
     </.cell_body>
@@ -431,7 +431,8 @@ defmodule LivebookWeb.SessionLive.CellComponent do
         <div class="p-4 max-w-full overflow-y-auto tiny-scrollbar">
           <%= render_output(output, %{
                 id: "cell-#{@cell_view.id}-evaluation#{evaluation_number(@cell_view.evaluation_status, @cell_view.number_of_evaluations)}-output#{index}",
-                socket: @socket
+                socket: @socket,
+                runtime: @runtime
               }) %>
         </div>
       <% end %>
@@ -483,17 +484,26 @@ defmodule LivebookWeb.SessionLive.CellComponent do
     )
   end
 
-  defp render_output({:error, formatted, :runtime_restart_required}, %{}) do
-    assigns = %{formatted: formatted}
+  defp render_output({:error, formatted, :runtime_restart_required}, %{runtime: runtime})
+       when runtime != nil do
+    assigns = %{formatted: formatted, is_standalone: Livebook.Runtime.standalone?(runtime)}
 
     ~H"""
     <div class="flex flex-col space-y-4">
       <%= render_error_message_output(@formatted) %>
-      <div>
-        <button class="button button-gray" phx-click="restart_runtime">
-          Restart runtime
-        </button>
-      </div>
+      <%= if @is_standalone do %>
+        <div>
+          <button class="button button-gray" phx-click="restart_runtime">
+            Restart runtime
+          </button>
+        </div>
+      <% else %>
+        <div class="text-red-600">
+          <span class="font-semibold">Note:</span>
+          This operation requires restarting the runtime, but we cannot
+          do it automatically for the current runtime
+        </div>
+      <% end %>
     </div>
     """
   end
diff --git a/lib/livebook_web/live/session_live/elixir_standalone_live.ex b/lib/livebook_web/live/session_live/elixir_standalone_live.ex
index d6853cd14..ea307f066 100644
--- a/lib/livebook_web/live/session_live/elixir_standalone_live.ex
+++ b/lib/livebook_web/live/session_live/elixir_standalone_live.ex
@@ -2,6 +2,7 @@ defmodule LivebookWeb.SessionLive.ElixirStandaloneLive do
   use LivebookWeb, :live_view
 
   alias Livebook.{Session, Runtime}
+  alias LivebookWeb.SessionLive.RuntimeHelpers
 
   @impl true
   def mount(_params, %{"session" => session, "current_runtime" => current_runtime}, socket) do
@@ -21,10 +22,9 @@ defmodule LivebookWeb.SessionLive.ElixirStandaloneLive do
           <%= @error_message %>
         </div>
       <% end %>
+      <RuntimeHelpers.default_runtime_note module={Runtime.ElixirStandalone} />
       <p class="text-gray-700">
         Start a new local node to handle code evaluation.
-        This is the default runtime and is started automatically
-        as soon as you evaluate the first cell.
       </p>
       <button class="button button-blue" phx-click="init">
         <%= if(matching_runtime?(@current_runtime), do: "Reconnect", else: "Connect") %>
diff --git a/lib/livebook_web/live/session_live/embedded_live.ex b/lib/livebook_web/live/session_live/embedded_live.ex
index 54f5f36c7..ba104dd16 100644
--- a/lib/livebook_web/live/session_live/embedded_live.ex
+++ b/lib/livebook_web/live/session_live/embedded_live.ex
@@ -2,16 +2,22 @@ defmodule LivebookWeb.SessionLive.EmbeddedLive do
   use LivebookWeb, :live_view
 
   alias Livebook.{Session, Runtime}
+  alias LivebookWeb.SessionLive.RuntimeHelpers
 
   @impl true
-  def mount(_params, %{"session" => session}, socket) do
-    {:ok, assign(socket, session: session)}
+  def mount(_params, %{"session" => session, "current_runtime" => current_runtime}, socket) do
+    if connected?(socket) do
+      Phoenix.PubSub.subscribe(Livebook.PubSub, "sessions:#{session.id}")
+    end
+
+    {:ok, assign(socket, session: session, current_runtime: current_runtime)}
   end
 
   @impl true
   def render(assigns) do
     ~H"""
     <div class="flex-col space-y-5">
+      <RuntimeHelpers.default_runtime_note module={Runtime.Embedded} />
       <p class="text-gray-700">
         Run the notebook code within the Livebook node itself.
         This is reserved for specific cases where there is no option
@@ -26,16 +32,26 @@ defmodule LivebookWeb.SessionLive.EmbeddedLive do
         may interfere with code from another notebook.
       </p>
       <button class="button button-blue" phx-click="init">
-        Connect
+        <%= if(matching_runtime?(@current_runtime), do: "Reconnect", else: "Connect") %>
       </button>
     </div>
     """
   end
 
+  defp matching_runtime?(%Runtime.Embedded{}), do: true
+  defp matching_runtime?(_runtime), do: false
+
   @impl true
   def handle_event("init", _params, socket) do
     {:ok, runtime} = Runtime.Embedded.init()
     Session.connect_runtime(socket.assigns.session.pid, runtime)
     {:noreply, socket}
   end
+
+  @impl true
+  def handle_info({:operation, {:set_runtime, _pid, runtime}}, socket) do
+    {:noreply, assign(socket, current_runtime: runtime)}
+  end
+
+  def handle_info(_message, socket), do: {:noreply, socket}
 end
diff --git a/lib/livebook_web/live/session_live/mix_standalone_live.ex b/lib/livebook_web/live/session_live/mix_standalone_live.ex
index b700f5732..7aecc2ccf 100644
--- a/lib/livebook_web/live/session_live/mix_standalone_live.ex
+++ b/lib/livebook_web/live/session_live/mix_standalone_live.ex
@@ -2,6 +2,7 @@ defmodule LivebookWeb.SessionLive.MixStandaloneLive do
   use LivebookWeb, :live_view
 
   alias Livebook.{Session, Runtime, Utils, FileSystem}
+  alias LivebookWeb.SessionLive.RuntimeHelpers
 
   @type status :: :initial | :initializing | :finished
 
@@ -26,6 +27,7 @@ defmodule LivebookWeb.SessionLive.MixStandaloneLive do
   def render(assigns) do
     ~H"""
     <div class="flex-col space-y-5">
+      <RuntimeHelpers.default_runtime_note module={Runtime.MixStandalone} />
       <p class="text-gray-700">
         Start a new local node in the context of a Mix project.
         This way all your code and dependencies will be available
diff --git a/lib/livebook_web/live/session_live/runtime_component.ex b/lib/livebook_web/live/session_live/runtime_component.ex
index 9bce49ad7..175e6f009 100644
--- a/lib/livebook_web/live/session_live/runtime_component.ex
+++ b/lib/livebook_web/live/session_live/runtime_component.ex
@@ -16,7 +16,8 @@ defmodule LivebookWeb.SessionLive.RuntimeComponent do
           if assigns.runtime do
             runtime_type(assigns.runtime)
           else
-            "elixir_standalone"
+            {runtime_module, _args} = Livebook.Config.default_runtime()
+            runtime_module |> struct() |> runtime_type()
           end
 
         Map.put(assigns, :type, type)
diff --git a/lib/livebook_web/live/session_live/runtime_helpers.ex b/lib/livebook_web/live/session_live/runtime_helpers.ex
new file mode 100644
index 000000000..0f242f9cd
--- /dev/null
+++ b/lib/livebook_web/live/session_live/runtime_helpers.ex
@@ -0,0 +1,22 @@
+defmodule LivebookWeb.SessionLive.RuntimeHelpers do
+  use Phoenix.Component
+
+  @doc """
+  Displays an info text if `@module` is the default runtime.
+  """
+  def default_runtime_note(assigns) do
+    ~H"""
+    <%= if default_runtime_module?(@module) do %>
+      <p class="text-gray-600 text-sm">
+        Note: This is the <span class="font-semibold">default runtime</span> and starts
+        automatically as soon as you evaluate the first cell.
+      </p>
+    <% end %>
+    """
+  end
+
+  defp default_runtime_module?(module) do
+    {default_module, _args} = Livebook.Config.default_runtime()
+    default_module == module
+  end
+end
diff --git a/lib/livebook_web/live/session_live/section_component.ex b/lib/livebook_web/live/session_live/section_component.ex
index a3f44dcc8..13536858e 100644
--- a/lib/livebook_web/live/session_live/section_component.ex
+++ b/lib/livebook_web/live/session_live/section_component.ex
@@ -96,6 +96,7 @@ defmodule LivebookWeb.SessionLive.SectionComponent do
             <%= live_component LivebookWeb.SessionLive.CellComponent,
                   id: cell_view.id,
                   session_id: @session_id,
+                  runtime: @runtime,
                   cell_view: cell_view %>
           <% end %>
 
diff --git a/test/livebook_web/live/session_live_test.exs b/test/livebook_web/live/session_live_test.exs
index 0ff0015d7..1195c3008 100644
--- a/test/livebook_web/live/session_live_test.exs
+++ b/test/livebook_web/live/session_live_test.exs
@@ -189,6 +189,10 @@ defmodule LivebookWeb.SessionLiveTest do
 
       Phoenix.PubSub.subscribe(Livebook.PubSub, "sessions:#{session.id}")
 
+      view
+      |> element("button", "Elixir standalone")
+      |> render_click()
+
       [elixir_standalone_view] = live_children(view)
 
       elixir_standalone_view
diff --git a/test/support/noop_runtime.ex b/test/support/noop_runtime.ex
index 64abb0375..645f71c7f 100644
--- a/test/support/noop_runtime.ex
+++ b/test/support/noop_runtime.ex
@@ -16,5 +16,6 @@ defmodule Livebook.Runtime.NoopRuntime do
     def drop_container(_, _), do: :ok
     def handle_intellisense(_, _, _, _, _), do: :ok
     def duplicate(_), do: {:ok, Livebook.Runtime.NoopRuntime.new()}
+    def standalone?(_runtime), do: false
   end
 end