Underlying any understanding of the mode, tempo, and relative importance of the adaptive process in the evolution of natural populations is the notion of whether adaptation is mutation-limited. Two very different population genetic models have recently been proposed in which the rate of adaptation is not strongly limited by the rate at which newly arising beneficial mutations enter the population. This review discusses the theoretical underpinnings and requirements of these models, as well as the experimental insights on the parameters of relevance. Importantly, empirical and experimental evidence to date challenges the recent enthusiasm for invoking these models to explain observed patterns of variation in humans and Drosophila .