This chapter provides a broad and selective introduction to diverse literatures on computational approaches to cultural dynamics. It explains the social psychological models of cultural dynamics, and then move to two prominent approaches to cultural dynamics— Axelrod's model of cultural dissemination and evolutionary game theoretic approaches to evolution of cooperation. These approaches focus on complementary aspects of cultural dynamics, and that each has unique strengths in dealing with some aspects, but not others. The Axelrod model has been used to explore the dynamics deriving from transmissions of cultural information and the role of drift and to some extent of importation; however, it does not address invention, or most importantly, selection. The evolutionary game theoretic approaches have a unique strength in examining the importance of the selection process in cultural evolution. The chapter discusses how the existing approaches complement each other, and also point to the gap in the existing theory— neither has addressed the process of invention.