Evolutionary game theory is a formal framework which enables one to model how behaviour in large populations might develop. One of the most promising features of evolutionary game theory is that by assuming agents follow simple rules of thumb, equilibria can emerge as the end result of a dynamic process, rather than just as a static, self-enforcing prescription of play. This in turn allows path-dependent predictions to be made on which equilibrium will be reached. The concept of stochastic stability (Foster and Young, 1990), allows a unique equilibrium to be selected if one also accepts that that the above simple rules of thumb are subject to occasional errors. My dissertation consists of four essays discussing various aspects of evolutionary models, in particular focusing on equilibrium selection in a new class of games. Chapter 1 proposes a new class of stage games, Multiple-Group Games (MGG), which extends existing frameworks by allowing more than one type of pairwise interaction. This surprisingly unstudied feature complicates the analysis slightly but is necessary for describing certain settings with large numbers of heterogeneous agents. Chapter 2 studies a particular MGG with two groups, The Language Game, in which all pairs of players potentially interact. In particular it focuses on stochastically stable equilibria when the rules of thumb that players follow are myopic best response, and the manner in which they err is uniform. It is shown that three properties affect equilibrium selection: group size, group payoffs, and rates of response. Chapter 3 looks at The Language Game where all pairs of players are not necessarily connected. It is shown that network architecture immediately affects the set of stochastically stable equilibria. This result seems intuitive and should be contrasted with the homogeneous agent models, in which network structure has no effect on equilibrium selection. Chapter 4, though technically a paper on equilibrium refinements, examines the ways in which players might make mistakes. It places a simple and reasonable constraint on the set of ways that players may err: if strategy A performs worse against the current population behaviour than strategy B, then strategy A is less likely to be played.