Increased expression of both FGF proteins and their receptors observed in many cancers is often associated with the development of chemoresistance, limiting the effectiveness of currently used anti-cancer therapies. Malfunctioning of the FGF/FGFR axis in cancer cells generates a number of molecular mechanisms that may affect the sensitivity of tumors to the applied drugs. Of key importance is the deregulation of cell signaling, which can lead to increased cell proliferation, survival, and motility, and ultimately to malignancy. Signaling pathways activated by FGFRs inhibit apoptosis, reducing the cytotoxic effect of some anti-cancer drugs. FGFRs-dependent signaling may also initiate angiogenesis and EMT, which facilitates metastasis and also correlates with drug resistance. Therefore, treatment strategies based on FGF/FGFR inhibition (using receptor inhibitors, ligand traps, monoclonal antibodies, or microRNAs) appear to be extremely promising. However, this approach may lead to further development of resistance through acquisition of specific mutations, metabolism switching, and molecular cross-talks. This review brings together information on the mechanisms underlying the involvement of the FGF/FGFR axis in the generation of drug resistance in cancer and highlights the need for further research to overcome this serious problem with novel therapeutic strategies.