Proteins are finicky molecules; they are barely stable and are prone to aggregate, but they must function in a crowded environment that is full of degradative enzymes bent on their destruction. It is no surprise that many common diseases are due to missense mutations that affect protein stability and aggregation. Here we review the literature on biophysics as it relates to molecular evolution, focusing on how protein stability and aggregation affect organismal fitness. We then advance a biophysical model of protein evolution that helps us to understand phenomena that range from the dynamics of molecular adaptation to the clock-like rate of protein evolution.