One of the most puzzling aspects of high temperature superconductors is that the metallic state out of which superconductivity appears is itself very unusual. Almost all we know about metals, semiconductors and superconductors relies on a picture of weakly interacting electrons. In the 1950's Landau explained why this was a good starting point despite the strong Coulomb forces that exist. His `Fermi liquid theory' is the `Standard Model' of condensed matter physics. The high temperature superconductors are one of a growing number of systems where this `Standard Model' is failing.
I will review a number of theoretical approaches to understanding metallic systems where a completely new description is required, without electron-like particles. Ideas including the splitting up of the electron's spin and charge or the formation of new types of excitation in strongly correlated quantum fluids.
Non-Fermi liquids A. J. Schofield, Contemporary Physics, 40, 95 (1999).