The behavior of three-dimensional bosonic gases at low temperatures is characterized
by the formation of a Bose-Einstein condensate (BEC), a macroscopic occupation of a
single-particle state. I will describe some universal scaling properties of bosonic
gases in the BEC phase. I will focus on the phase-coherence properties, illustrating
the crossover from the 3D behavior to the effective 1D behavior of very elongated systems,
and on the critical behavior arising at the spatial boundary of an inhomogeneous system.
Universal predictions are confirmed by quantum Monte Carlo simulations of the 3D Bose-Hubbard
model, a realistic model of bosonic atoms in optical lattices.