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Cold atomic gases have provided us with a great number of opportunities forstudying various physical systems under controlled conditions that are seldomoffered in other fields. We are thus at the point where one can truly doquantum simulation of models that are relevant for instance in condensed-matteror high-energy physics, i.e. we are on the verge of a 'cool' quantum simulatoras envisioned by Feynman. One of the avenues under exploration is the physicsof one-dimensional systems. Until recently this was mostly in the many-bodylimit but now experiments can be performed with controllable particle numbersall the way down to the few-body regime. After a brief introduction to some ofthe relevant experiments, I will review recent theoretical work onone-dimensional quantum systems containing bosons, fermions, or mixtures of thetwo, with a particular emphasis on the case where the particles are held by anexternal trap.

Exploring the few- to many-body crossover using cold atoms in one dimension