25 years after their discovery, the microscopic problem of high Tc superconductivity in cuprates is still not “solved”. I will focus on summarizing the experiments that show us that the observed phases, with varying carrier concentration, challenge three paradigms of 20th century condensed matter physics. (i) The parent Mott insulator cannot be understood within band theory; (ii) the superconducting state and phase transition force us to go beyond a BCS mean-field description; and (iii) the “normal” metallic state cannot be described within Landau Fermi liquid theory. I will then briefly describe some of the success in theoretically understanding the superconducting state and indicate open questions about the normal state.