The emergence of robust methods to expand the genetic code allows incorporation of non-canonical amino acids into the polypeptide chain of proteins, thus making it possible to introduce unnatural chemical functionalities in enzymes. In this Perspective, we show how this powerful methodology is used to create enzymes with improved and novel, even new-to-nature, catalytic activities. We provide an overview of the current state of the art, and discuss the potential benefits of developing and using enzymes with genetically encoded non-canonical amino acids compared with enzymes containing only canonical amino acids. Genetic incorporation of unnatural amino acids into proteins broadens the possibilities of enzyme design. This Perspective discusses the exciting opportunities for biocatalysis offered by this method — such as new-to-nature catalytic activities — and potential benefits over classical enzyme engineering.