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 of Li-6 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.