The main forces directing long-term molecular evolution remain obscure. A sizable fraction of amino-acid substitutions seem to be fixed by positive selection, but it is unclear to what degree long-term protein evolution is constrained by epistasis, that is, instances when substitutions that are accepted in one genotype are deleterious in another. Here we obtain a quantitative estimate of the prevalence of epistasis in long-term protein evolution by relating data on amino-acid usage in 14 organelle proteins and 2 nuclear-encoded proteins to their rates of short-term evolution. We studied multiple alignments of at least 1,000 orthologues for each of these 16 proteins from species from a diverse phylogenetic background and found that an average site contained approximately eight different amino acids. Thus, without epistasis an average site should accept two-fifths of all possible amino acids, and the average rate of amino-acid substitutions should therefore be about three-fifths lower than the rate of neutral evolution. However, we found that the measured rate of amino-acid substitution in recent evolution is 20 times lower than the rate of neutral evolution and an order of magnitude lower than that expected in the absence of epistasis. These data indicate that epistasis is pervasive throughout protein evolution: about 90 per cent of all amino-acid substitutions have a neutral or beneficial impact only in the genetic backgrounds in which they occur, and must therefore be deleterious in a different background of other species. Our findings show that most amino-acid substitutions have different fitness effects in different species and that epistasis provides the primary conceptual framework to describe the tempo and mode of long-term protein evolution.