Evolutionary Game Theory is the study of strategic interactions among large populations of agents who base their decisions on simple, myopic rules. A major goal of the theory is to determine broad classes of decision procedures which both provide plausible descriptions of selfish behaviour and include appealing forms of aggregate behaviour. For example, properties such as the correlation between strategiesą growth rates and payoffs, the connection between stationary states and the well-known game theoretic notion of Nash equilibria, as well as global guarantees of convergence to equilibrium, are widely studied in the literature. Our paper can be seen as a quick introduction to Evolutionary Game Theory, together with a new research result and a discussion of many algorithmic and complexity open problems in the area. In particular, we discuss some algorithmic and complexity aspects of the theory, which we prefer to view more as Game Theoretic Aspects of Evolution rather than as Evolutionary Game Theory, since the term “evolution” actually refers to strategic adaptation of individualsą behaviour through a dynamic process and not the traditional evolution of populations. We consider this dynamic process as a self-organization procedure which, under certain conditions, leads to some kind of stability and assures robustness against invasion. In particular, we concentrate on the notion of the Evolutionary Stable Strategies (ESS). We demonstrate their qualitative difference from Nash Equilibria by showing that symmetric 2-person games with random payoffs have on average exponentially less ESS than Nash Equilibria. We conclude this article with some interesting areas of future research concerning the synergy of Evolutionary Game Theory and Algorithms.