Key issues in theories of high temperature superconductors

High temperature superconductivity in cuprate superconductors remains an unsolved problem in theoretical physics. The same statement can also be made about a number of other superconductors that have been dubbed unconventional. What makes these superconductors so elusive is an interesting question in itself. The present manuscript focuses on the recent magnetic oscillation experiments and how they fit into the broader picture. Many aspects of these experiments can be explained by Fermi liquid theory; the key issue is the extent to which this is true. If true, the entire paradigm developed over the past three decades must be reexamined. A critical analysis of this issue has necessitated a broader analysis of questions about distinct ground states of matter, which may be useful in understanding other unconventional superconductors.