  Particles with short-range interactions and a large scattering length have
universal low-energy properties that do not depend on the details of their
structure or their interactions at short distances. In the 2-body sector, the
universal properties are familiar and depend only on the scattering length a.
In the 3-body sector for identical bosons, the universal properties include the
existence of a sequence of shallow 3-body bound states called "Efimov states"
and log-periodic dependence of scattering observables on the energy and the
scattering length. The spectrum of Efimov states in the limit a -> +/- infinity
is characterized by an asymptotic discrete scaling symmetry that is the
signature of renormalization group flow to a limit cycle. In this review, we
present a thorough treatment of universality for the system of three identical
bosons and we summarize the universal information that is currently available
for other 3-body systems. Our basic tools are the hyperspherical formalism to
provide qualitative insights, Efimov's radial laws for deriving the constraints
from unitarity, and effective field theory for quantitative calculations. We
also discuss topics on the frontiers of universality, including its extension
to systems with four or more particles and the systematic calculation of
deviations from universality.
