  Bose-Einstein condensation is a unique phase transition in that it is not
driven by inter-particle interactions, but can theoretically occur in an ideal
gas, purely as a consequence of quantum statistics. This chapter addresses the
question \emph{`How is this ideal Bose gas condensation modified in the
presence of interactions between the particles?' } This seemingly simple
question turns out to be surprisingly difficult to answer. Here we outline the
theoretical background to this question and discuss some recent measurements on
ultracold atomic Bose gases that have sought to provide some answers.
