  Single- and multi-band Hubbard models have been found to describe many of the
complex phenomena that are observed in the cuprate and iron-based
high-temperature superconductors. Simulations of these models therefore provide
an ideal framework to study and understand the superconducting properties of
these systems and the mechanisms responsible for them. Here we review recent
dynamic cluster quantum Monte Carlo simulations of these models, which provide
an unbiased view of the leading correlations in the system. In particular, we
discuss what these simulations tell us about superconductivity in the
homogeneous 2D single-orbital Hubbard model, and how charge stripes affect this
behavior. We then describe recent simulations of a bilayer Hubbard model, which
provides a simple model to study the type and nature of pairing in systems with
multiple Fermi surfaces such as the iron-based superconductors.
