Due to their exceptional electrical, thermal, and optical properties, low-dimensional (LD) materials are very promising for many applications, such as nanoelectronic devices, energy storage, energy conversion, and thermal management. The thermal performance of LD materials is often an important consideration in these applications. Although freestanding LD materials exhibit interesting thermal properties, they are almost never used in such a form. Instead, they are often integrated into a certain environment; for example, in a composite material or on a substrate. Due to the large surface-to-volume ratio of LD materials, the environment usually has a strong impact on the thermal transport properties of these materials. The thermal behavior of the LD materials can be completely different from the freestanding form. The effect of environmental perturbation on thermal transport properties has recently attracted a lot of research interest. In this article, we aim to provide a comprehensive review of how the typical external perturbations, including tensile strain, substrate, and clustering, can affect the thermal transport properties of LD materials. Emphasis will be placed on how these perturbations affect the lattice structure, phonon dispersion, lattice anharmonicity, and thermal conductivity. We will also summarize the achievements and the remaining challenges on this research topic.