Among the liveliest disputes in evolutionary biology today are disputes concerning the role of chance in evolution--more specifically, disputes concerning the relative evolutionary importance of natural selection vs. so-called "random drift". The following discussion is an attempt to sort out some of the broad issues involved in those disputes. In the first half of this paper, I try to explain the differences between evolution by natural selection and evolution by random drift. On some common construals of "natural selection", those two (...) modes of evolution are completely indistinguishable. Even on a proper construal of "natural selection", it is difficult to distinguish between the "improbable results of natural selection" and evolution by random drift. In the second half of this paper, I discuss the variety of positions taken by evolutionists with respect to the evolutionary importance of random drift vs. natural selection. I will then consider the variety of issues in question in terms of a conceptual distinction often used to describe the rise of probabilistic thinking in the sciences. I will argue, in particular, that what is going on here is not, as might appear at first sight, just another dispute about the desirability of "stochastic" vs. "deterministic" theories. Modern evolutionists do not argue so much about whether evolution is stochastic, but about how stochastic it is. (shrink)