Information update and real-world action suggest a universe of changing models, where finding the valid dynamic laws involves logical languages with modalities for model change. I will discuss two families of such dynamic modal logics, stating some typical results, as well as open problems.

Dynamic-epistemic logics add dynamic superstructure to existing static logics, and tend to not increase complexity of satisfiability and model checking. Logics of graph change, arising e.g. in the study of games or of languages that change their own models under evaluation, tend to jump to higher complexities, becoming undecidable or worse. I will report some recent results that zoom in on the border line between the two kinds of system, and end with some issues about redesign and restoring decidability for more complex logics of action and information dynamics.