Modal Logic: A Semantic Perspective Johan van Benthem, Patrick Blackburn Abstract: This is a chapter in the forthcoming "Handbook of Modal Logic", written as an introduction to the modus operandi of keeping a balance between expressive power and complexity found in modal languages. With this theme as a running thread, we survey the basic model theory of modal logic over both models and frames, as well as basic results on complexity. Against this background, we provide a uniform look at many well-known modal formalisms, including epistemic, dynamic, temporal, and conditional logic. Finally, although our main emphasis is on relational models: i.e., graphs, we also discuss the major alternative semantics. Keywords: modal logic; definability; complexity; ; bisimulation; extended modal languages; ; frame correspondence; alternative semantics