We review the various factors that limit adaptation by natural selection. Recent discussion of constraints on selection and, conversely, of the factors that enhance “evolvability”, have concentrated on the kinds of variation that can be produced. Here, we emphasise that adaptation depends on how the various evolutionary processes shape variation in populations. We survey the limits that population genetics places on adaptive evolution, and discuss the relationship between disparate literatures. BioEssays 22:1075–1084, 2000. © 2000 John Wiley & Sons, Inc.