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This is the content of the lectures given by the author at the winter schoolKAWA3 held at the University of Barcelona in 2012 from January 30 to  February 3. The main goal was to give an account of viscosity techniques andto apply them to degenerate Complex Monge-Amp\`ere equations following recentworks of P. Eyssidieux, V. Guedj and the author.  We will survey the main techniques used in the viscosity approach and showhow to adapt them to degenerate complex Monge-Amp\`ere equations.  The heart of the matter in this approach is the "Comparison Principle" whichallows us to prove uniqueness of solutions.  We will prove a global viscosity comparison principle for degenerate complexMonge-Amp\`ere equations on compact K\"ahler manifolds and show how to combineViscosity methods and Pluripotential methods to get "continuous versions" ofthe Calabi-Yau and Aubin-Yau Theorems in some degenerate situations. Inparticular we prove the existence of singular K\"ahler-Einstein metrics withcontinuous potentials on compact normal K\"ahler varieties with mildsingularities and ample or trivial canonical divisor.

A viscosity approach to degenerate complex Monge-Amp\`ere equations