This chapter introduces the most important classes of games underlying practical security models. These include Stackelberg games, Nash games, signaling games, and games with distribution-valued payoffs. The latter build upon empirical methods and data science to construct games from data, but also reveals theoretic connections to multi-criteria optimization using lexicographic goal priorities (that classical games cannot deal with, but distribution-valued games can handle). Each game description is accompanied by examples from the security domain to motivate and illustrate the use of the individual model. Each class of game is discussed in relation to the other types, highlighting pros and cons, las well as applications, detailed in later chapters.