High selectivities and exquisite control over reaction outcomes entice chemists to use biocatalysts in organic synthesis. However, many useful reactions are not accessible because they are not in nature’s known repertoire. We will use this review to outline an evolutionary approach to engineering enzymes to catalyze reactions not found in nature. We begin with examples of how nature has discovered new catalytic functions and how such evolutionary progressions have been recapitulated in the laboratory starting from extant enzymes. We then examine non-native enzyme activities that have been discovered and exploited for chemical synthesis, emphasizing reactions that do not have natural counterparts. The new functions have mechanistic parallels to the native reaction mechanisms that often manifest as catalytic promiscuity and the ability to convert from one function to the other with minimal mutation. We present examples of how non-natural activities have been improved by directed evolution, mimicking the process used by nature to create new catalysts. Examples of new enzyme functions include epoxide opening reactions with non-natural nucleophiles catalyzed by a laboratory-evolved halohydrin dehalogenase, cyclopropanation and other carbene transfer reactions catalyzed by cytochrome P450 variants, and non-natural modes of cyclization by a modified terpene synthase. Lastly, we describe discoveries of non-native catalytic functions that may provide future opportunities for expanding the enzyme universe.