This paper develops a logic that combines the main features of dynamic epistemic logic with those of inquisitive semantics. We argue that this merge helps both traditions a step further. From the viewpoint of dynamic epistemic logic, the main benefit lies in the fact that inquisitiveness does not only enter the picture at the level of speech acts, but already at the level of semantic content, which means in particular that it becomes possible to deal with embedded questions. From the viewpoint of inquisitive semantics, the main vantage point is that we inherit from dynamic epistemic logic a perspicuous way of representing the epistemic states of the conversational participants, and a way to specify explicitly how utterances and other speech acts affect these epistemic states.