New methods are revealing the character of epistatic interactions within proteins and their impacts on evolution. Variation in biochemical phenotypes across protein sequences is determined primarily by the context-independent effects of amino acids and global nonlinearities imposed by biophysical mechanisms. Specific epistasis — primarily pairwise interactions — plays a subsidiary role, but collectively has a major impact on evolution. Every substitution in an evolving protein changes the effects of many potential mutations at epistatically coupled sites. As homologs diverge from common ancestors, the constraints that determine the accessibility of subsequent mutations gradually drift apart. Opportunities for adaptation and functional innovation also change over time, because each substitution epistatically modifies the effects of mutations on existing and new protein phenotypes. Over moderate evolutionary timescales, the outcomes of protein evolution — both their sequences and biochemical properties — thus become strongly contingent on the substitutions that happen to occur in each lineage. This interplay between random chance and each proteins’ epistatic architecture helps explain widely observed lineage-specific patterns of conservation and variation that are not expected under the dominant schools of thought in molecular evolution.