An organism's body size tells us a lot about how it makes a living, suggesting that body size is a key parameter in evolution. We outline three large-scale trends in body size evolution. Bergmann's Rule is the tendency for warm-blooded species at high latitudes to be larger than their close relatives nearer the equator. The Island Rule is the trend for small species to become larger, and large species smaller, on islands. Cope's Rule, which we discuss in much more detail, is the tendency for lineages to increase in size over evolutionary time. Trends are best studied by combining data on evolutionary relationships among species with fossil information on how characters have changed through time. After highlighting some methodological pitfalls that can trap unwary researchers, we summarise evidence that Cope's Rule, while not being by any means universal, has operated in some very different animal groups - from microfauna (single-celled Foraminifera) to megafauna (dinosaurs) - and we discuss the possibility that natural selection and clade selection may pull body size in opposite directions. Despite size's central importance, there is little evidence that body size differences among related groups affect their evolutionary success: careful comparisons rarely reveal any correlation between size and present-day diversity. We end by touching on human impacts, which are often more severe on larger species.