Theories of adaptation: what they do and don't say

Theoretical work on adaptation has lagged behind experimental. But two classes of adaptation model have been partly explored. One is phenotypic and the other DNA sequence based. I briefly consider an example of each - Fisher's geometric model and Gillespie's mutational landscape model, respectively - reviewing recent results. Despite their fundamental differences, these models give rise to several strikingly similar results. I consider possible reasons for this congruence. I also emphasize what predictions do and, as important, do not follow from these models.