Analogies between biological and cultural evolution date back to Darwin, yet the analogies have remained loose. Neutral evolution, known to be important in biology, has been proposed as a null model for cultural change, but has not developed into tests for selection on cultural features. Using inference in timeseries of alternative word forms and grammatical constructions, I demonstrate a cultural analog of natural selection on a background of netural evolution. Social evolution, on the other hand, implies selection in a social environment and therefore cannot be described with a neutral model. I propose a model of pure frequency-dependent selection as a generic null model for social evolution, and use the model to illustrate diverse effects of social selection. I derive a non-linear form of frequency-dependent selection from a mechanistic model of mate choice and show unintuitive consequences for evolutionary dynamics. I infer complex forms of frequency dependent selection—including positive and negative frequency-dependent selection at different frequencies—from data regarding the copying of baby names, the fashions of dog breeds, and the use of rare languages, and discuss the implications for cultural diversity.