  The Hubbard model is the simplest model of interacting fermions on a lattice
and is of similar importance to correlated electron physics as the Ising model
is to statistical mechanics or the fruit fly to biomedical science. Despite its
simplicity, the model exhibits an incredible wealth of phases, phase
transitions, and exotic correlation phenomena. While analytical methods have
provided a qualitative description of the model in certain limits, numerical
tools have shown impressive progress in achieving quantitative accurate results
over the last years. This article gives an introduction to the model, motivates
common questions, and illustrates the progress that has been achieved over the
last years in revealing various aspects of the correlation physics of the
model.
