  This is a short review of the theoretical work on the two-dimensional Hubbard
model performed in Sherbrooke in the last few years. It is written on the
occasion of the twentieth anniversary of the discovery of high-temperature
superconductivity. We discuss several approaches, how they were benchmarked and
how they agree sufficiently with each other that we can trust that the results
are accurate solutions of the Hubbard model. Then comparisons are made with
experiment. We show that the Hubbard model does exhibit d-wave
superconductivity and antiferromagnetism essentially where they are observed
for both hole and electron-doped cuprates. We also show that the pseudogap
phenomenon comes out of these calculations. In the case of electron-doped high
temperature superconductors, comparisons with angle-resolved photoemission
experiments are nearly quantitative. The value of the pseudogap temperature
observed for these compounds in recent photoemission experiments has been
predicted by theory before it was observed experimentally. Additional
experimental confirmation would be useful. The theoretical methods that are
surveyed include mostly the Two-Particle Self-Consistent Approach, Variational
Cluster Perturbation Theory (or variational cluster approximation), and
Cellular Dynamical Mean-Field Theory.
