  In recent years, the combination of advanced quantum Monte Carlo (QMC)
methods and local interactions derived from chiral effective field theory (EFT)
has been shown to provide a versatile and systematic approach to nuclear
systems. Calculations at next-to-next-to-leading order in chiral EFT have lead
to fascinating results for nuclei and nucleonic matter. On the one hand,
ground-state properties of nuclei are well reproduced up to $A\leq16$, even
though these potentials have been fit to nucleon-nucleon scattering and
few-body observables only. On the other hand, a reasonable description of
neutron-matter properties emerges. While regulator functions applied to two-
and three-nucleon forces are a necessary ingredient in these many-body
calculations, the use of local regulators leads to a substantial residual
regulator and cutoff dependence that increases current theoretical
uncertainties. In this contribution, we review local chiral interactions, their
applications, and QMC results for nuclei and neutron matter. In addition, we
address regulator issues for such potentials and present a possible path
forward.
