Despite the astonishing breadth of enzymes in nature, no enzymes are known for many of the valuable catalytic transformations discovered by chemists. Recent work in enzyme design and evolution, however, gives us good reason to think that this will change. We describe a chemomimetic biocatalysis approach that draws from small-molecule catalysis and synthetic chemistry, enzymology, and molecular evolution to discover or create enzymes with non-natural reactivities. We illustrate how cofactor-dependent enzymes can be exploited to promote reactions first established with related chemical catalysts. The cofactors can be biological, or they can be non-biological to further expand catalytic possibilities. The ability of enzymes to amplify and precisely control the reactivity of their cofactors together with the ability to optimize non-natural reactivity by directed evolution promises to yield exceptional catalysts for challenging transformations that have no biological counterparts.