diff --git a/lib/livebook/application.ex b/lib/livebook/application.ex
index 5c7a2d614..e1f7ab637 100644
--- a/lib/livebook/application.ex
+++ b/lib/livebook/application.ex
@@ -119,6 +119,7 @@ defmodule Livebook.Application do
     end
   end
 
+  @spec invalid_hostname!(String.t()) :: no_return()
   defp invalid_hostname!(prelude) do
     Livebook.Config.abort!("""
     #{prelude}, which indicates something wrong in your OS configuration.
diff --git a/lib/livebook/notebook.ex b/lib/livebook/notebook.ex
index 4ddf3e7e1..e8ce1c0f7 100644
--- a/lib/livebook/notebook.ex
+++ b/lib/livebook/notebook.ex
@@ -226,7 +226,7 @@ defmodule Livebook.Notebook do
   @doc """
   Updates cells as `update_cells/2`, but carries an accumulator.
   """
-  @spec update_reduce_cells(t(), acc, ({Cell.t(), acc} -> {Cell.t(), acc})) :: t()
+  @spec update_reduce_cells(t(), acc, (Cell.t(), acc -> {Cell.t(), acc})) :: {t(), acc}
         when acc: term()
   def update_reduce_cells(notebook, acc, fun) do
     {sections, acc} =
@@ -441,8 +441,8 @@ defmodule Livebook.Notebook do
   The cells are not ordered in any secific way.
   """
   @spec cell_ids_with_children(t(), list(Cell.id())) :: list(Cell.id())
-  def cell_ids_with_children(data, parent_cell_ids) do
-    graph = cell_dependency_graph(data.notebook)
+  def cell_ids_with_children(notebook, parent_cell_ids) do
+    graph = cell_dependency_graph(notebook)
 
     for parent_id <- parent_cell_ids,
         leaf_id <- Graph.leaves(graph),
diff --git a/lib/livebook/session.ex b/lib/livebook/session.ex
index 952110d6c..e23e84eac 100644
--- a/lib/livebook/session.ex
+++ b/lib/livebook/session.ex
@@ -1266,7 +1266,7 @@ defmodule Livebook.Session do
   end
 
   defp extract_archive!(binary, path) do
-    :ok = :erl_tar.extract({:binary, binary}, [:compressed, {:cwd, path}])
+    :ok = :erl_tar.extract({:binary, binary}, [:compressed, {:cwd, String.to_charlist(path)}])
   end
 
   @doc """
diff --git a/lib/livebook/session/data.ex b/lib/livebook/session/data.ex
index 37d784913..4cf015685 100644
--- a/lib/livebook/session/data.ex
+++ b/lib/livebook/session/data.ex
@@ -847,7 +847,7 @@ defmodule Livebook.Session.Data do
     |> set!(
       notebook: Notebook.add_cell_output(data.notebook, cell.id, output),
       input_values:
-        {-1, output}
+        {0, output}
         |> Cell.Elixir.find_inputs_in_output()
         |> Map.new(fn attrs -> {attrs.id, attrs.default} end)
         |> Map.merge(data.input_values)
@@ -1521,7 +1521,7 @@ defmodule Livebook.Session.Data do
           uniq: true,
           do: cell.id
 
-    cell_ids = Notebook.cell_ids_with_children(data, evaluable_cell_ids)
+    cell_ids = Notebook.cell_ids_with_children(data.notebook, evaluable_cell_ids)
 
     for {cell, _} <- elixir_cells_with_section,
         cell.id in cell_ids,
diff --git a/lib/livebook_web/controllers/session_controller.ex b/lib/livebook_web/controllers/session_controller.ex
index 7eeb65ea8..f1f7049c7 100644
--- a/lib/livebook_web/controllers/session_controller.ex
+++ b/lib/livebook_web/controllers/session_controller.ex
@@ -114,7 +114,7 @@ defmodule LivebookWeb.SessionController do
     # The request comes from a cross-origin iframe
     conn = allow_cors(conn)
 
-    case lookup_asset(hash, file_parts) do
+    case lookup_asset(hash, asset_path) do
       {:ok, local_asset_path} ->
         conn
         |> put_content_type(asset_path)
diff --git a/lib/livebook_web/live/home_live.ex b/lib/livebook_web/live/home_live.ex
index 9e0c4a7f1..3a06b2b17 100644
--- a/lib/livebook_web/live/home_live.ex
+++ b/lib/livebook_web/live/home_live.ex
@@ -85,7 +85,7 @@ defmodule LivebookWeb.HomeLive do
             </.live_component>
           </div>
 
-          <div class="py-12">
+          <div class="py-12" data-element="explore-section">
             <div class="mb-4 flex justify-between items-center">
               <h2 class="uppercase font-semibold text-gray-500">
                 Explore
diff --git a/lib/livebook_web/live/session_live.ex b/lib/livebook_web/live/session_live.ex
index 3c3d98b51..314ed2e2c 100644
--- a/lib/livebook_web/live/session_live.ex
+++ b/lib/livebook_web/live/session_live.ex
@@ -3,7 +3,7 @@ defmodule LivebookWeb.SessionLive do
 
   import LivebookWeb.UserHelpers
   import LivebookWeb.SessionHelpers
-  import Livebook.Utils, only: [access_by_id: 1, format_bytes: 1]
+  import Livebook.Utils, only: [format_bytes: 1]
 
   alias LivebookWeb.SidebarHelpers
   alias Livebook.{Sessions, Session, Delta, Notebook, Runtime, LiveMarkdown}
@@ -1453,10 +1453,8 @@ defmodule LivebookWeb.SessionLive do
       {:report_cell_revision, _pid, _cell_id, _revision} ->
         data_view
 
-      {:apply_cell_delta, _pid, cell_id, _delta, _revision} ->
-        data_view
-        |> update_cell_view(data, cell_id)
-        |> update_dirty_status(data)
+      {:apply_cell_delta, _pid, _cell_id, _delta, _revision} ->
+        update_dirty_status(data_view, data)
 
       # For outputs that update existing outputs we send the update directly
       # to the corresponding component, so the DOM patch is isolated and fast.
@@ -1490,17 +1488,6 @@ defmodule LivebookWeb.SessionLive do
     end
   end
 
-  defp update_cell_view(data_view, data, cell_id) do
-    {:ok, cell, section} = Notebook.fetch_cell_and_section(data.notebook, cell_id)
-    cell_view = cell_to_view(cell, data)
-
-    put_in(
-      data_view,
-      [:section_views, access_by_id(section.id), :cell_views, access_by_id(cell.id)],
-      cell_view
-    )
-  end
-
   defp prune_outputs(%{private: %{data: data}} = socket) do
     assign_private(
       socket,
diff --git a/test/livebook/intellisense_test.exs b/test/livebook/intellisense_test.exs
index d50533268..9251346c6 100644
--- a/test/livebook/intellisense_test.exs
+++ b/test/livebook/intellisense_test.exs
@@ -1,11 +1,11 @@
-defmodule Livebook.IntellisenseTest.Utils do
-  @moduledoc false
+defmodule Livebook.IntellisenseTest do
+  use ExUnit.Case, async: true
 
-  @doc """
-  Returns intellisense context resulting from evaluating
-  the given block of code in a fresh context.
-  """
-  defmacro eval(do: block) do
+  alias Livebook.Intellisense
+
+  # Returns intellisense context resulting from evaluating
+  # the given block of code in a fresh context.
+  defmacrop eval(do: block) do
     quote do
       block = unquote(Macro.escape(block))
       binding = []
@@ -21,14 +21,6 @@ defmodule Livebook.IntellisenseTest.Utils do
       }
     end
   end
-end
-
-defmodule Livebook.IntellisenseTest do
-  use ExUnit.Case, async: true
-
-  import Livebook.IntellisenseTest.Utils
-
-  alias Livebook.Intellisense
 
   describe "format_code/1" do
     test "formats valid code" do
diff --git a/test/livebook/sessions_test.exs b/test/livebook/sessions_test.exs
index b58e9a594..ac8777f84 100644
--- a/test/livebook/sessions_test.exs
+++ b/test/livebook/sessions_test.exs
@@ -1,5 +1,5 @@
 defmodule Livebook.SessionsTest do
-  use ExUnit.Case
+  use ExUnit.Case, async: true
 
   alias Livebook.Sessions
 
diff --git a/test/livebook_web/live/explore_live_test.exs b/test/livebook_web/live/explore_live_test.exs
index e91c78006..88c03732f 100644
--- a/test/livebook_web/live/explore_live_test.exs
+++ b/test/livebook_web/live/explore_live_test.exs
@@ -1,5 +1,5 @@
 defmodule LivebookWeb.ExploreLiveTest do
-  use LivebookWeb.ConnCase
+  use LivebookWeb.ConnCase, async: true
 
   import Phoenix.LiveViewTest
 
diff --git a/test/livebook_web/live/home_live_test.exs b/test/livebook_web/live/home_live_test.exs
index f34abb386..d68fd5c8a 100644
--- a/test/livebook_web/live/home_live_test.exs
+++ b/test/livebook_web/live/home_live_test.exs
@@ -1,5 +1,5 @@
 defmodule LivebookWeb.HomeLiveTest do
-  use LivebookWeb.ConnCase
+  use LivebookWeb.ConnCase, async: true
 
   import Phoenix.LiveViewTest
 
@@ -206,7 +206,7 @@ defmodule LivebookWeb.HomeLiveTest do
 
     assert {:error, {:live_redirect, %{to: to}}} =
              view
-             |> element(~s{a}, "Welcome to Livebook")
+             |> element(~s{[data-element="explore-section"] a}, "Welcome to Livebook")
              |> render_click()
              |> follow_redirect(conn)
 
diff --git a/test/livebook_web/live/session_live_test.exs b/test/livebook_web/live/session_live_test.exs
index 7ea8836ae..143fb8141 100644
--- a/test/livebook_web/live/session_live_test.exs
+++ b/test/livebook_web/live/session_live_test.exs
@@ -1,5 +1,5 @@
 defmodule LivebookWeb.SessionLiveTest do
-  use LivebookWeb.ConnCase
+  use LivebookWeb.ConnCase, async: true
 
   import Phoenix.LiveViewTest
 
@@ -37,7 +37,7 @@ defmodule LivebookWeb.SessionLiveTest do
       wait_for_session_update(session.pid)
 
       # Wait for LV to update
-      render(view)
+      _ = render(view)
 
       assert page_title(view) =~ "My notebook"
     end
@@ -319,8 +319,12 @@ defmodule LivebookWeb.SessionLiveTest do
 
       wait_for_session_update(session.pid)
 
-      assert render(view) =~ "Updated frame"
-      refute render(view) =~ "In frame"
+      # Render once, so that frame send_update is processed
+      _ = render(view)
+
+      content = render(view)
+      assert content =~ "Updated frame"
+      refute content =~ "In frame"
     end
   end