  We review the infrared behavior of interacting bosons at zero temperature.
After a brief discussion of the Bogoliubov approximation and the breakdown of
perturbation theory due to infrared divergences, we present two approaches that
are free of infrared divergences -- Popov's hydrodynamic theory and the
non-perturbative renormalization group -- and allow us to obtain the exact
infrared behavior of the correlation functions. We also point out the
connection between the infrared behavior in the superfluid phase and the
critical behavior at the superfluid--Mott-insulator transition in the
Bose-Hubbard model.
