Form factors provide some of the most direct insight into the structure of hadrons. For mesons and hyperons, none of which are available as targets, form factor measurements can only be made for timelike momentum transfers by means of e+e- -> hhbar reactions, where h can be any hadron. Further, only for large momentum transfers the measurements can be hopefully understood in terms of QCD, or more realistically in terms of pQCD. We have made precision measurements of the form factors of pions, kaons, protons, and all the neutral and charged hyperons, lambda, sigma, cascade, and omega, at the large momentum transfers of 14.2 and 17.4 GeV^2. The results reveal unexpected features, and pose serious questions for pQCD and the role of SU(3)- breaking.