The performance and reliability of thermoelectric materials and devices based on low-dimensional materials are strongly influenced by heat dissipation and thermal stability, which are directly linked to the thermal conductivity of the materials. Therefore, accurate determination of the thermal properties remains a critical aspect of material development efforts, which requires the continuous advancement and refinement of the measurement techniques. In recent years, substantial progress has been achieved in theoretical and experimental approaches for the characterization of thermal conductivity in low-dimensional materials. This article reviews these advances, focusing on recent developments in the measurement of thermal conductivity in thin films, two-dimensional materials, and other nanostructures. The fundamental concepts underlying a range of experimental and theoretical techniques are presented together with their theoretical framework, underscoring the critical role of selecting a measurement approach appropriate to the sample thickness, thermal conductivity regime, and material characteristics. Special attention is paid to the thermal conductivity of emerging materials relevant for thermal management, including carbon-based materials, black phosphorus, MXenes, and boron nitride. Furthermore, the advantages and limitations of the different measurement techniques are discussed, in relation to the type and structure of the material under study. Finally, the review summarizes the key findings and outlines future research opportunities, highlighting promising directions across different classes of low-dimensional materials.