The present invention provides methods and compositions that may be used to modulate binding of a fibroblast growth factor (FGF) polypeptide to an FGF receptor (FGFR). In preferred embodiments, the methods and compositions of the invention modulate binding of a particular FGF polypeptide, the FGF4 polypeptide, to its receptor. The invention provides, in particular, variant FGF polypeptides that have at least one amino acid residue substitutions, insertion or deletion which alters the polypeptdies' binding affinity for an FGFR. The invention also provides models for the three-dimensional structure of a dimerized complex of FGF-FGFR-heparin. Using these models, key amino acid residues are identified and novel compounds (including novel variants of FGF and FGFR) can be identified which modulate FGF binding to its receptor. Such new compounds are therefore useful, e.g., as agonist and antagonist for FGF signaling and for bioactivities associated therewith.