Do cultural phenomena undergo evolutionary change, in a Darwinian sense? If so, is evolutionary game theory (EGT) the best way to study them? Opinion on these questions is sharply divided. Proponents of EGT argue that it offers a unified theoretical framework for the social sciences, while critics even deny that Darwinian models are appropriately applied to culture. To evaluate these claims, we examine three facets of cultural evolution: (i) cultural traits that evolve by Darwinian selection, (ii) cultural traits that affect biological fitness, and (iii) coevolution of culture and biology, where selection in one affects evolutionary outcomes in the other. For each of these cases, the relevance of EGT depends on whether its assumptions are met. Those assumptions are quite restrictive: selection is constant, time horizons are deep, the external environment is not part of the game, and neutral processes such as drift are irrelevant. If these conditions are not met, other evolutionary models such as neutrality, coalescence theory, or niche construction may prove more appropriate. We conclude that Darwinian processes can occur in all three types of cultural or biological change. However, exclusive reliance on EGT can obscure the respective roles of selective and neutral processes.