This book is an exploration of current trends in logical theories of information flow across various fields, such as belief revision in computer science and dynamic semantics in linguistics. It provides one mathematical perspective encompassing all of these fields. This framework generates a new agenda of questions concerning dynamic inference and dynamic operators. The result is a mathematical theory of process models, simulations between these, and modal languages over them, which is developed in detail. New results include theorems on expressive completeness, representation of styles of inference, and new kinds of decidable remodeling for standard logics.