  Significant advances in numerical techniques have enabled recent
breakthroughs in the study of various properties of the Hubbard model - a
seemingly simple, yet complex model of correlated electrons that has been a
focus of study for more than half a century. In particular, it captures the
essence of strong correlations, and is believed to possess various emergent,
low energy states and collective excitations characteristic of cuprate
high-temperature superconducting materials. While a thorough review of all
activity is not possible here, we have focused the discussion on our recent
work using unbiased, numerically exact, ``brute force", finite temperature
quantum Monte Carlo methods. Our various studies reveal a rich variety of
quantum liquid crystal phases, and complementary transport properties, which
answer some questions, but certainly raise others concerning ``strange metal"
behavior and the ultimate fate of quasiparticles in the Hubbard model.
