  Over the past two decades, advances in computational algorithms have revealed
a curious property of the two-dimensional Hubbard model (and related theories)
with hole doping: the presence of close-in-energy competing ground states that
display very different physical properties. On the one hand, there is a
complicated state exhibiting intertwined spin, charge, and pair density wave
orders. We call this `type A'. On the other hand, there is a uniform d-wave
superconducting state that we denote as `type B'. We advocate, with the support
of both microscopic theoretical calculations and experimental data, dividing
the high-temperature cuprate superconductors into two corresponding families,
whose properties reflect either the type A or type B ground states at low
temperatures. We review the anomalous properties of the pseudogap phase that
led us to this picture, and present a modern perspective on the role that
umklapp scattering plays in these phenomena in the type B materials. This
reflects a consistent framework that has emerged over the last decade, in which
Mott correlations at weak coupling drive the formation of the pseudogap. We
discuss this development, recent theory and experiments, and open issues.
