This book is an exploration of current trends in logical theories of information flow across various fields, such as belief revision in computer science or dynamic semantics in linguistics. It provides one mathematical perspectives encompassing all of these. 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 quite some detail. New results include theorems on expressive completedness, representation of styles of inference, and new kinds of decidable remodeling for standard logics. This theory is also confronted with practice in computer science, linguistics and philosophy.