It is now well established that cultural evolution is a fundamentally Darwinian process, exhibiting incremental descent with modification, semi-random innovation (trial and error), competition among ideas, selective survival and other Darwinian features. One key ingredient of Darwinian evolution is genetic recombination, usually through sexual reproduction, which makes evolution a cumulative phenomenon. Accounts of cultural evolution have generally neglected the need to identify an equivalent to genetic recombination. I argue that the common human habit of exchanging objects and services has the same effect on cultural evolution as sex does on biological evolution, making it cumulative. The lack of exchange explains why culture evolves more slowly and does not become cumulative in other species and in some isolated human populations.