Cuprate superconductors from the viewpoint of strong correlation

There is now a growing consensus that the physics of cuprate superconductors is dominated by strong correlation and that the fundamental challenge to the theorist is to achieve an understanding of the doped Mott-Hubbard insulator. From this viewpoint, the Hubbard and the t-J models are reasonable Hamiltonians to study. I shall review the gauge theory description of the t-J model. I shall discuss two recent advances: 1) the study of bosons in a strongly fluctuating gauge field in collaboration with Derek Lee and Don Kim, and 2) the description of the underdoped regime, focusing on the photoemission spectra and the relation, to the spin gap phenomenon, in collaboration with Xiao-Gang Wen.