Local chiral effective field theory interactions have recently been developed and used in the context of quantum Monte Carlo few-and many-body methods for nuclear physics. In this work, we go over detailed features of local chiral nucleon-nucleon interactions and examine their effect on properties of the deuteron, paying special attention to the perturbativeness of the expansion. We then turn to three-nucleon interactions, focusing on operator ambiguities and their interplay with regulator effects. We then discuss the nuclear Green's function Monte Carlo method, going over both wave-function correlations and approximations for the two-and three-body propagators. Following this, we present a range of results on light nuclei: Binding energies and distribution functions are contrasted and compared, starting from several different microscopic interactions.