Gluon saturation and initial conditions for relativistic heavy ion collisions

We present an overview of theoretical aspects of the phenomenon of gluon saturation in high energy scattering in Quantum Chromo Dynamics. Then we review the state-of-the-art of saturation-based phenomenological approaches to the study and characterization of the initial state of ultra-relativistic heavy ion collisions performed at RHIC and the LHC. Our review focuses mostly in the Color Glass Condensate effective theory, although we shall also discuss other approaches in parallel.