  We present a field-theory description of ultracold bosonic atoms in presence
of a disordered external potential. By means of functional integration
techniques, we aim to investigate and review the interplay between disordered
energy landscapes and fluctuations, both thermal and quantum ones. Within the
broken-symmetry phase, up to the Gaussian level of approximation, the disorder
contribution crucially modifies both the condensate depletion and the
superfluid response. Remarkably, it is found that the ordered (i.e. superfluid)
phase can be destroyed also in regimes where the random external potential is
suitable for a perturbative analysis. We analyze the simplest case of quenched
disorder and then we move to present the implementation of the replica trick
for ultracold bosonic systems. In both cases, we discuss strengths and
limitations of the reviewed approach, paying specific attention to possible
extensions and the most recent experimental outputs.
