A renormalization group analysis of interacting Fermion systems shows that there are two fundamentally different fixed points, Landau Fermi liquid theory and what has been called ‘‘Luttinger Liquid Theory’’ by Haldane, a type of state in which fluctuations of different quantum numbers—e.g., charge and spin—acquire distinct spectra, and Fermi surface correlations have unusual exponents. The luttinger liquids comprise most interacting 1‐dimensional systems, and some higher‐dimensional systems in which, as in the Hubbard model, the band spectrum is bounded above. All higher‐dimensional systems with true Mott‐Hubbard gaps and an upper Hubbard band, including most 2d Hubbard models, are Luttinger liquids. We summarize the experimental evidence in favor of the 2d Hubbard model for highTcsuperconductors and the constraints pointing towards its non‐Fermi liquid nature. We describe progress towards explaining normal state and superconducting properties and elucidating the highTcmechanism.