In recent decades a burgeoning literature has documented the cultural transmission of behavior through social learning in numerous vertebrate and invertebrate species. One meaning of ‘cultural evolution in animals’ refers to these discoveries, and I present an overview of key findings. I then address the other meaning of the term focused on cultural changes within a lineage. Such changes in humans, described as ‘cumulative cultural evolution’, have been spectacular, but relatively little attention has yet been paid to the topic in non-human animals, other than asserting the process is unique to humans. A variety of evidence including both controlled experiments and field observations has begun to challenge this view, and in some behavioral domains, notably birdsong, cultural evolution has been studied for many years. Here I dissect concepts of cultural evolution and cumulative culture and appraise the accumulating evidence bearing on their nature and significance for evolutionary biology at large.