 Modal logic is a rich and complex subject matter. This entry does not present a complete survey of all the systems developed and of all the model theoretic results proved in the lapse of time under consideration. It does however offer a meaningful survey of the main systems aiming to be useful to those looking for an historical outline of the subject matter that, even if not all-inclusive, delineates the most interesting model theoretic results and indicates further lines of exploration. Bull and Segerberg’s (1984: 3) useful division of the original sources of modal logic into three distinct traditions—syntactic, algebraic, and model theoretic—is adopted. For other less influential traditions, see Bull and Segerberg (1984: 16). See also Lindström and Segerberg’s “Modal Logic and Philosophy” (2007). The main focus of this entry is on propositional modal logic, while only some particular aspects of the semantics of quantified modal logic are briefly discussed. For a more detailed treatment of quantified modal logic, consult the SEP entry on  modal logic.  Concerning the entry’s notation, notice that \(\Rightarrow\) is adopted in place of Lewis’s fishhook for strict implication, and \(\Leftrightarrow\) for strict equivalence.