  The discovery of high temperature superconductivity in the cuprates in 1986
triggered a spectacular outpouring of creative and innovative scientific
inquiry. Much has been learned over the ensuing 28 years about the novel forms
of quantum matter that are exhibited in this strongly correlated electron
system. This progress has been made possible by improvements in sample quality,
coupled with the development and refinement of advanced experimental
techniques. In part, avenues of inquiry have been motivated by theoretical
developments, and in part new theoretical frameworks have been conceived to
account for unanticipated experimental observations. An overall qualitative
understanding of the nature of the superconducting state itself has been
achieved, while profound unresolved issues have come into increasingly sharp
focus concerning the astonishing complexity of the phase diagram, the
unprecedented prominence of various forms of collective fluctuations, and the
simplicity and insensitivity to material details of the "normal" state at
elevated temperatures. New conceptual approaches, drawing from string theory,
quantum information theory, and various numerically implemented approximate
approaches to problems of strong correlations are being explored as ways to
come to grips with this rich tableaux of interrelated phenomena.
