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.

冷原子气体已成为探索基础物理的范例系统，同时允许在量子技术中的应用。该领域的加速发展催生了一套非常先进的工程技术，例如，可以调整相互作用、塑造外部几何形状、在大量具有不同属性的原子种类中进行选择，或者控制原子数量。特别是，可以在较低维度下运行并将原子系统驱动到强相关状态。在这篇综述中，我们从理论角度讨论了低维少体冷原子系统的最新进展。我们主要关注一维的玻色子系统，并在回顾由相关性的存在激发的量子动力学过程的最新研究之前，介绍静态特性。除了讨论这些系统中出现的基本物理现象外，我们还概述了常用的计算和数值工具和方法，从而对该领域进行了平衡和全面的概述。最后，我们对这些相关系统中值得探索的未来可能方向进行了展望。