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The achievement of Bose-Einstein condensation in ultra-cold vapours
of alkali atoms has given enormous impulse to the study of dilute
atomic gases in condensed quantum states inside magnetic traps and
optical lattices. High purity and easy optical access make them
ideal candidates to investigate fundamental issues on interacting
quantum systems. This review presents some theoretical issues which
have been addressed in this area and the numerical techniques which
have been developed and used to describe them, from mean-field
models to classical and quantum simulations for equilibrium and
dynamical properties. The attention given in this article to
methods beyond standard mean-field approaches should make it a
useful reference point for future advances in these areas.
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