Fibroblast growth factor receptors (FGFRs) are recognized therapeutic targets in cancer. We here describe insights underpinning the impact of mutations on FGFR1 and FGFR3 kinase activity and drug efficacy, using a combination of computational calculations and experimental approaches including cellular studies, X-ray crystallography and biophysical and biochemical measurements. Our findings reveal that some of the tested compounds, in particular TKI258, could provide therapeutic opportunity not only for patients with primary alterations in FGFR but also for acquired resistance due to the gatekeeper mutation. The accuracy of the computational methodologies applied here shows a potential for their wider application in studies of drug binding and in assessments of functional and mechanistic impacts of mutations, thus assisting efforts in precision medicine.