Study of the e+e- annihilation into the proton-antiproton pair began 40 years ago. However, the first accurate measurement of the e+e- --> p anti-p cross section in a wide energy region was performed only in 2005 by the BABAR detector using the initial-state radiation method. This measurement was based on about half of data collected in the BABAR experiment. In this talk, I will present the final BABAR analysis of e+e- --> p anti-p based on the full data sample. The e+e- --> p anti-p cross section and the proton effective electromagnetic form factor have been measured from threshold up to 4.5 GeV. Below 3 GeV the ratio of the electric and magnetic form factors has been extracted from the analysis of the proton angular distribution. The charge asymmetry in the angular distribution has been also studied. The BABAR results are compared with existing data from e+e- and p anti-p annihilation experiments. Future measurements of the proton electromagnetic form factors will be briefly discussed.