The cavity method is a mathematical method presented by Marc Mézard, Giorgio Parisi and Miguel Angel Virasoro in 1987 to solve some mean field type models in statistical physics, specially adapted to disordered systems. The method has been used to compute properties of ground states in many condensed matter and optimization problems. The cavity method has proved useful in the solution of optimization problems such as k-satisfiability and graph coloring. It has yielded not only ground states energy predictions in the average case, but also has inspired algorithmic methods.