Protein evolution underpins life, and understanding its behavior as a system is of great importance. However, our current models of protein evolution are arguably too simplistic to allow quantitative interpretation and prediction of evolutionary trajectories. Viewing protein evolution as a complex system has the potential to advance our understanding and ability to model protein evolution. In this perspective, we discuss aspects of protein evolution that are typical of complex systems, from nonlinear dynamics, sensitivity to initial conditions, self-organization, and the emergence of order from chaos and disorder. We discuss how the growth in sequence and structural data, insights from laboratory evolution and new machine learning tools can advance the study of protein evolution and that by treating protein evolution as a complex adaptive system, we may gain new insights into the fundamental principles driving biological innovation and adaptation and apply this to protein engineering and design.

Protein Evolution as a Complex System