Females of many species mate with multiple males, thereby inciting competition among ejaculates from rival males for fertilization. In response to increasing sperm competition, males are predicted to enhance their investment in sperm production. This prediction is so widespread that testes size (correcting for body size) is commonly used as a proxy of sperm competition, even in the absence of any other information about a species' reproductive behaviour. By contrast, a debate about whether sperm competition selects for smaller or larger sperm has persisted for nearly three decades, with empirical studies demonstrating every possible response. Here, we synthesize nearly 40 years of sperm competition research in a meta-analytical framework to determine how the evolution of sperm number (i.e. testes size) and sperm size (i.e. sperm head, midpiece, flagellum and total length) is influenced by varying levels of sperm competition across species. Our findings support the long-held assumption that higher levels of sperm competition are associated with relatively larger testes. We also find clear evidence that sperm competition is associated with increases in all components of sperm length. We discuss these results in the context of different theoretical predictions and general patterns in the breeding biology and selective environment of sperm. This article is part of the theme issue 'Fifty years of sperm competition'.