The renormalization group (RG) describes the change of a physical system due to smoothing or averaging out microscopic details when going to a lower resolution. This brings into play a notion of scale dependence for the action functionals of interest. Infinitesimal RG transformations map actions to nearby ones, thus giving rise to a vector field on theory space. The scale dependence of an action is encoded in a "running" of the coupling constants parametrizing this action, { g α α } ≡ ≡ { g α α ( k ) } , with the RG scale k . This gives rise to a trajectory in theory space (RG trajectory), describing the evolution of an action functional with respect to the scale. Which of all possible trajectories is realized in Nature has to be determined by measurements.