Fibroblast growth factor (FGF) plays an important role in human embryogenesis, angiogenesis, cell proliferation, and differentiation. Carcinogenesis is accompanied by aberrant constitutive activation of FGF receptors (FGFRs) resulting from missense mutation in the FGFR1-4 genes, generation of chimeric oncogenes, FGFR1-4 gene amplification, alternative splicing shift toward formation of mesenchymal FGFR isoforms, and FGFR overexpression. Altogether, these alterations contribute to auto- and paracrine stimulation of cancer cells and neoangiogenesis. Certain missense mutations are found at a high rate in urinary bladder cancer and can be used for non-invasive cancer recurrence diagnostics by analyzing urine cell pellet DNA. Chimeric FGFR1/3 and amplified FGFR1/2 genes can predict cell response to the targeted therapy in various oncological diseases. In recent years, high-throughput sequencing has been used to analyze exomes of virtually all human tumors, which allowed to construct phylogenetic trees of clonal cancer evolution with special emphasis on driver mutations in FGFR1-4 genes. At present, FGFR blockers, such as multi-kinase inhibitors, specific FGFR inhibitors, and FGF ligand traps are being tested in clinical trials. In this review, we discuss current data on the functioning of the FGFR family proteins in both normal and cancer cells, mutations in the FGFR1-4 genes, and mechanisms underlying their oncogenic potential, which might be interesting to a broad range of scientists searching for specific tumor markers and targeted anti-cancer drugs.