In the past few decades, scholars from several disciplines have pursued the curious parallel noted by Darwin between the genetic evolution of species and the cultural evolution of beliefs, skills, knowledge, languages, institutions, and other forms of socially transmitted information. Here, I review current progress in the pursuit of an evolutionary science of culture that is grounded in both biological and evolutionary theory, but also treats culture as more than a proximate mechanism that is directly controlled by genes. Both genetic and cultural evolution can be described as systems of inherited variation that change over time in response to processes such as selection, migration, and drift. Appropriate differences between genetic and cultural change are taken seriously, such as the possibility in the latter of nonrandomly guided variation or transformation, blending inheritance, and one-to-many transmission. The foundation of cultural evolution was laid in the late 20th century with population-genetic style models of cultural microevolution, and the use of phylogenetic methods to reconstruct cultural macroevolution. Since then, there have been major efforts to understand the sociocognitive mechanisms underlying cumulative cultural evolution, the consequences of demography on cultural evolution, the empirical validity of assumed social learning biases, the relative role of transformative and selective processes, and the use of quantitative phylogenetic and multilevel selection models to understand past and present dynamics of society-level change. I conclude by highlighting the interdisciplinary challenges of studying cultural evolution, including its relation to the traditional social sciences and humanities.