The renormalization group (RG) consists of a set of concepts and methods which can be used to analyze phenomena in many different fields of mathematics and physics, ranging from probability theory and statistical mechanics, to nonequilibrium phenomena. These RG techniques are particularly useful in order to study fluctuations on top of a mean-field like solution. In the last two decades the development of the so-called functional renormalization group (FRG) method has provided a mathematically elegant and yet simple way of expressing Wilson’s idea of successive mode elimination in terms of a formally exact functional differential equation for the effective action (also known as the Ginzburg-Landau free energy in condensed matter contexts).