Methods, apparatus, systems, and computer-readable media are provided for transferring dialog sessions between devices using deep links. The dialog sessions can correspond to interactions, mediated by an automated assistant, between a user and a third party application. During the dialog session, a user can request that the dialog session be transferred to a different device, for example, to interact with the third party application through a different modality. In response, the automated assistant and/or the third party application can generate a link that can be transferred to the transferee device to allow the transferee device to seamlessly take over the dialog session. In this way, computational resources and electrical power can be preserved by not requiring a recipient device to re-process natural language inputs previously provided during the dialog session.