We report a recent lattice-QCD calculation of nucleon and pion electromagnetic form factors and nucleon axial form factors, with special emphasis on large Q 2 . Conventional lattice form-factor calculations can only reach about 2.5 GeV 2 , but in this work the transfer momentum is pushed as large as 6 GeV 2 . Here, we demonstrate the results on 2+1-flavor anisotropic clover lattices for the nucleon and pion, comparing with low-Q 2 quantities, such as Dirac and Pauli radii, anomalous magnetic moments, g A and M A . Our approach can be applied to isotropic lattices and lattices with smaller lattice spacing to achieve even larger-Q 2 form factors. The form factors are processed to obtain transverse charge and magnetization densities across 2-dimensional impact-parameter space. These measurements could give important theoretical input to experiments, such as those of JLab's 12-GeV program, and provide insight into hadronic structure.