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.
I will review the status of the understanding of metallic quantum
criticality, and the recent progress made by QMC simulations, focusing
on the cases of spin density wave and Ising nematic criticality. The
results obtained so far will be described, as well as 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.