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The thermal conductivity of a material or device is dependent on its characteristic dimension. When the characteristic dimension is commensurate to the mean free paths of thermal energy carriers, the thermal conductivity decreases. The precise relationship between characteristic size and thermal conductivity, which depends on the distribution of energy carrier mean free paths in the material, is not straightforward to determine experimentally. The utility of this relationship has led many researchers to study the mean free path dependent contributions of thermal energy carriers to the thermal conductivity of materials, known as the thermal conductivity accumulation function. This review highlights a number of recent experimental results and techniques used to study the thermal conductivity accumulation function, including transient thermal grating, time domain thermoreflectance, and broadband frequency domain thermoreflectance. In these techniques, nondiffusive thermal transport is induced (i.e., thermal gradients occur over length scales comparable to energy carrier mean free paths) and an effective thermal conductivity of the material is determined. We conclude with our outlook on future directions for the field focused on improved interpretations of the experiments and new materials with unique mean free path distributions. [ABSTRACT FROM AUTHOR]