In this talk I will discuss recent quantum oscillation experiments in both electron and hole doped high temperature superconductors in high fields and low temperatures. The range of experiments involve oscillations of Hall coefficient, Shubnikov-de Haas oscillations, de Haas-von Alphen oscillations and oscillations of the specific heat. I shall provide a theoretical framework based on concepts of Fermi liquids and broken symmetries in the ground state that was previously thought to be impossible in the relevant regime of these superconductors. These ideas are antithetical to the prevalent notion of these materials being in the proximity of a Mott insulating phase.