Enzymes have been evolving to catalyze new chemical reactions for billions of years, and will continue to do so for billions more. Here, we review examples in which evolutionary biochemists have used big data and high-throughput experimental tools to shed new light on the enormous functional diversity of extant enzymes, and the evolutionary processes that gave rise to it. We discuss the role that gene loss has played in enzyme evolution, as well as the more familiar processes of gene duplication and divergence. We also review insightful studies that relate not only catalytic activity, but also a host of other biophysical and cellular parameters, to organismal fitness. Finally, we provide an updated perspective on protein engineering, based on our new-found appreciation that most enzymes are sloppy and mediocre.