  Cold atomic gases have become a paradigmatic system for exploring fundamental
physics, which at the same time allows for applications in quantum
technologies. The accelerating developments in the field have led to a highly
advanced set of engineering techniques that, for example, can tune
interactions, shape the external geometry, select among a large set of atomic
species with different properties, or control the number of atoms. In
particular, it is possible to operate in lower dimensions and drive atomic
systems into the strongly correlated regime. In this review, we discuss recent
advances in few-body cold atom systems confined in low dimensions from a
theoretical viewpoint. We mainly focus on bosonic systems in one dimension and
provide an introduction to the static properties before we review the
state-of-the-art research into quantum dynamical processes stimulated by the
presence of correlations. Besides discussing the fundamental physical phenomena
arising in these systems, we also provide an overview of the calculational and
numerical tools and methods that are commonly used, thus delivering a balanced
and comprehensive overview of the field. We conclude by giving an outlook on
possible future directions that are interesting to explore in these correlated
systems.
