Information exchange can be seen as a dynamic process of raising and resolving issues. The goal of this paper is to provide a logical framework to model and reason about this process. We develop an inquisitive dynamic epistemic logic (IDEL), which enriches the standard framework of dynamic epistemic logic (DEL), incorporating insights from recent work on inquisitive semantics. At a static level, IDEL does not only allow us to model the information available to a set of agents, like standard epistemic logic, but also the issues that the agents entertain. At a dynamic level, IDEL does not only allow us to model the effects of communicative actions that provide new information, like standard DEL, but also the effects of actions that raise new issues. Thus, IDEL provides the fundamental tools needed to analyze information exchange as a dynamic process of raising and resolving issues.