  Few-body physics related to the Efimov effect is discussed using the
functional renormalization group method. After a short review of
renormalization in its modern formulation we apply this formalism to the
description of scattering and bound states in few-body systems of identical
bosons and distinguishable fermions with two and three components. The Efimov
effect leads to a limit cycle in the renormalization group flow. Recently
measured three-body loss rates in an ultracold Fermi gas $^6$Li atoms are
explained within this framework. We also discuss briefly the relation to the
many-body physics of the BCS-BEC crossover for two-component fermions and the
formation of a trion phase for the case of three species.
