The modern field of cultural evolution is now over 30 years old, and an extensive body of theory and data has been amassed. This article reviews models of cultural evolution, both experimental and theoretical, and surveys what they can tell us about cultural evolutionary processes. The models are grouped according to which of four broad questions they address: (1) How are cultural traits changed during transmission? (2) How and why do cultural traits accumulate over time? (3) What social learning biases do people use? and (4) What are the population?level consequences of different social learning biases? We conclude by highlighting gaps in the literature and promising future research directions, including the further integration of theoretical models and experimental data, the identification of the factors underlying cumulative cultural evolution, and the explanation of individual and cultural variation in social learning biases.