  Lattice simulations of QCD have produced precise estimates for the masses of
the lowest-lying hadrons which show excellent agreement with experiment. By
contrast, lattice results for the vector and axial vector form factors of the
nucleon show significant deviations from their experimental determination. We
present results from our ongoing project to compute a variety of form factors
with control over all systematic uncertainties. In the case of the pion
electromagnetic form factor we employ partially twisted boundary conditions to
extract the pion charge radius directly from the linear slope of the form
factor near vanishing momentum transfer. In the nucleon sector we focus
specifically on the possible contamination from contributions of higher excited
states. We argue that summed correlation functions offer the possibility of
eliminating this source of systematic error. As an illustration of the method
we discuss our results for the axial charge, gA, of the nucleon.
