This paper presents recent results concerning the existence and qualitative
properties of travelling wave solutions to the Gross-Pitaevskii equation posed
on the whole space R^N. Unlike the defocusing nonlinear Schr\"odinger equations
with null condition at infinity, the presence of non-zero conditions at
infinity yields a rather rich and delicate dynamics. We focus on the case N = 2
and N = 3, and also briefly review some classical results on the
one-dimensional case. The works we survey provide rigorous justifications to
the impressive series of results which Jones, Putterman and Roberts established
by formal and numerical arguments
