We introduce a dynamic epistemic logic that is based on what an agent can observe, including joint observation and observation of what other agents observe. This generalizes van der Hoek, Wooldridge and colleague’s logics ECL-PC(PO) and LRC where it is common knowledge which propositional variables each agent observes. In our logic, facts of the world and their observability can both be modified by assignment programs. We show how epistemic operators can be interpreted in this framework and identify the conditions under which the principles of positive and negative introspection are valid. We also provide a sound and complete axiomatization and prove that the satisfiability problem is PSpace-complete. Finally, we show how public and private announcements can be expressed and illustrate the latter by the gossip spreading problem.