Methods, apparatus, and computer readable media related to interaction between a user and an automated assistant during a dialog between the user and the automated assistant. Some implementations are directed to adapting a graphical and/or audible presentation of search results provided by the automated assistant for presentation to the user. The adaptation may be in response to attribute(s), of one or more of the search results, referenced in spoken and/or typed textual input provided by the user during the dialog. Some of those implementations may enable a user to provide textual input to navigate the search results within the dialog and within resource and/or interface constraints associated with the dialog. Some of those implementations may additionally and/or alternatively enable adapting, based on textual input provided by a user to the automated assistant, when and/or whether search results having certain attributes are provided to the user by the automated assistant.