Abstract Engineered proteins are being widely developed and employed in applications ranging from enzyme catalysts to therapeutic antibodies. Directed evolution, an iterative experimental process composed of mutagenesis and library screening, is a powerful technique for enhancing existing protein activities and generating entirely new ones not observed in nature. However, the process of accumulating mutations for enhanced protein activity requires chemical and structural changes that are often destabilizing, and low protein stability is a significant barrier to achieving large enhancements in activity during multiple rounds of directed evolution. Here we highlight advances in understanding the origins of protein activity/stability trade‐offs for two important classes of proteins (enzymes and antibodies) as well as innovative experimental and computational methods for overcoming such trade‐offs. These advances hold great potential for improving the generation of highly active and stable proteins that are needed to address key challenges related to human health, energy and the environment.