Providing at least one contextually relevant suggestion to one or more users of an ongoing message exchange thread between the users. The suggestion is provided for presentation to the user(s) via user interface output device(s) of computing device(s) of the user(s). The suggestion indicates a query that can be submitted to an automated assistant to cause the automated assistant to incorporate, into the message exchange thread, content that is responsive to the query. In some implementations, the suggestion is a selectable suggestion and content that is responsive to the query is incorporated into the message exchange thread in response to user interface input that is directed to the selectable suggestion. In some implementations, the suggestion is determined based on one or more messages that have already been communicated between users of the message exchange thread.