Fibroblast growth factors (FGFs) and their receptors (FGFRs) regulate numerous cellular processes. Deregulation of FGFR signalling is observed in a subset of many cancers, making activated FGFRs a highly promising potential therapeutic target supported by multiple preclinical studies. However, early-phase clinical trials have produced mixed results with FGFR-targeted cancer therapies, revealing substantial complexity to targeting aberrant FGFR signalling. In this Review, we discuss the increasing understanding of the differences between diverse mechanisms of oncogenic activation of FGFR, and the factors that determine response and resistance to FGFR targeting.