Organisms vary widely in size, from microbes weighing 0.1 pg to trees weighing thousands of megagrams — a 10²¹-fold range similar to the difference in mass between an elephant and the Earth. Mass has a pervasive influence on biological processes, but the effect is usually non-proportional; for example, a tenfold increase in mass is typically accompanied by just a four- to sevenfold increase in metabolic rate. Understanding the cause of allometric scaling has been a long-standing problem in biology. Here, we examine the evolution of metabolic allometry in animals by linking microevolutionary processes to macroevolutionary patterns. We show that the genetic correlation between mass and metabolic rate is strong and positive in insects, birds and mammals. We then use these data to simulate the macroevolution of mass and metabolic rate, and show that the interspecific relationship between these traits in animals is consistent with evolution under persistent multivariate selection on mass and metabolic rate over long periods of time.