Micro- and nanoscale materials have remarkable mechanical properties, such as enhanced strength and toughness, but they usually display sample-to-sample fluctuations and size effects. These variations are a nuisance for engineering applications and an intriguing problem for science. Our understanding of size effects in small-scale materials has progressed in the past few years thanks to experimental measurements of carbon-based nanomaterials, such as graphene and carbon nanotubes, and of crystalline and amorphous micro- and nanopillars and micro- and nanowires. At the same time, increased computational power has allowed atomistic simulations to reach experimentally relevant sample sizes. From a theoretical point of view, the standard analysis and interpretation of experimental and computational data rely on traditional extreme value theories developed decades ago for macroscopic samples, with recent work extending some of the limiting assumptions of these theories to the micro- and nanoscale. In this Review, we discuss experimental and computational studies of size effects on the fracture in micro- and nanoscale materials, point out the advantages and limitations of existing theories and, finally, provide a pedagogical guide to the analysis of fracture data from micro- and nanoscale samples.