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Historical processes display some degree of "contingency," meaning their outcomes are sensitive to seemingly inconsequential events that can fundamentally change the future. Contingency is what makes historical outcomes unpredictable. Unlike many other natural phenomena, evolution is a historical process. Evolutionary change is often driven by the deterministic force of natural selection, but natural selection works upon variation that arises unpredictably through time by random mutation, and even beneficial mutations can be lost by chance through genetic drift. Moreover, evolution has taken place within a planetary environment with a particular history of its own. This tension between determinism and contingency makes evolutionary biology a kind of hybrid between science and history. While philosophers of science examine the nuances of contingency, biologists have performed many empirical studies of evolutionary repeatability and contingency. Here, we review the experimental and comparative evidence from these studies. Replicate populations in evolutionary "replay" experiments often show parallel changes, especially in overall performance, although idiosyncratic outcomes show that the particulars of a lineage's history can affect which of several evolutionary paths is taken. Comparative biologists have found many notable examples of convergent adaptation to similar conditions, but quantification of how frequently such convergence occurs is difficult. On balance, the evidence indicates that evolution tends to be surprisingly repeatable among closely related lineages, but disparate outcomes become more likely as the footprint of history grows deeper. Ongoing research on the structure of adaptive landscapes is providing additional insight into the interplay of fate and chance in the evolutionary process.