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We review the Resonating Valence Bond (RVB) theory of high temperatur esuperconductivity using Gutzwiller projected wave functions that incorporatestrong correlations. After a general overview of the phenomenon of hightemperature superconductivity, we discuss Anderson's RVB picture and itsimplementation by renormalised mean field theory (RMFT) and variational MonteCarlo (VMC) techniques. We review RMFT and VMC results with an emphasis onrecent development s in extending VMC and RMFT techniques to excited states. Wecompare results obtained from these methods with angle resolved photoemissionspectroscopy (ARPES) and scanning tunnelling microscopy (STM). We conclude bysummarising recent successes of this approach and discuss open problems thatneed to be solved for a consistent and complete description of high temperaturesuperconductivity using Gutzwiller projected wave functions.

Gutzwiller-RVB Theory of High Temperature Superconductivity: Results from Renormalised Mean Field Theory and Variational Monte Carlo Calculations