diff --git a/lib/kino/bridge.ex b/lib/kino/bridge.ex
index d0d9f804..1e64856c 100644
--- a/lib/kino/bridge.ex
+++ b/lib/kino/bridge.ex
@@ -62,9 +62,18 @@ defmodule Kino.Bridge do
   Note that the input must be known to Livebook, otherwise
   an error is returned.
   """
-  @spec get_input_value(String.t()) :: {:ok, term()} | {:error, :not_found} | request_error()
+  @spec get_input_value(String.t()) ::
+          {:ok, term()} | {:error, :not_found} | {:error, :bad_process} | request_error()
   def get_input_value(input_id) do
-    with {:ok, reply} <- io_request({:livebook_get_input_value, input_id}), do: reply
+    pid = self()
+
+    io_request_result =
+      with {:request_error, :unsupported} <-
+             io_request({:livebook_get_input_value, input_id, pid}),
+           # Livebook <= v0.13.2 does not support the request with pid
+           do: io_request({:livebook_get_input_value, input_id})
+
+    with {:ok, reply} <- io_request_result, do: reply
   end
 
   @doc """
diff --git a/lib/kino/input.ex b/lib/kino/input.ex
index 1731454a..93116520 100644
--- a/lib/kino/input.ex
+++ b/lib/kino/input.ex
@@ -746,6 +746,14 @@ defmodule Kino.Input do
         raise "failed to read input value, input not found." <>
                 " Make sure to render the input before reading its value"
 
+      {:error, :bad_process} ->
+        raise "input value can only be read in the main evaluation process," <>
+                " but Kino.Input.read/1 was called by another process." <>
+                " You can read the input value upfront and pass it to the process." <>
+                " In case you want to read the latest input value from a long-running" <>
+                " process, consider using Kino.Control.form/2, or subscribing to the" <>
+                " input change using one of the functions in the Kino.Control module"
+
       {:request_error, reason} ->
         raise "failed to read input value, reason: #{inspect(reason)}"
     end