  Metallic quantum critical phenomena are believed to play a key role in many
strongly correlated materials, including high temperature superconductors.
Theoretically, the problem of quantum criticality in the presence of a Fermi
surface has proven to be highly challenging. However, it has recently been
realized that many models used to describe such systems are amenable to
numerically exact solution by quantum Monte Carlo (QMC) techniques, without
suffering from the fermion sign problem. In this article, we review the status
of the understanding of metallic quantum criticality, and the recent progress
made by QMC simulations. We focus on the cases of spin density wave and Ising
nematic criticality. We describe the results obtained so far, and their
implications for superconductivity, non-Fermi liquid behavior, and transport in
the vicinity of metallic quantum critical points. Some of the outstanding
puzzles and future directions are highlighted.
