Thermal transport plays a crucial role in performance and reliability of semiconductor electronic devices, where heat is mainly carried by phonons. Phonon transport in crystalline semiconductor materials, such as Si, Ge, GaAs, GaN, etc, has been extensively studied over the past two decades. In fact, study of phonon physics in crystalline semiconductor materials in both bulk and nanostructure forms has been the cornerstone of the emerging field of 'nanoscale heat transfer'. On the contrary, thermal properties of amorphous materials have been relatively less explored. Recently, however, a growing number of studies have re-examined the thermal properties of amorphous semiconductors, such as amorphous Si. These studies, which included both computational and experimental work, have revealed that phonon transport in amorphous materials is perhaps more complicated than previously thought. For instance, depending on the type of amorphous materials, thermal transport occurs via three types of vibrations: propagons, diffusons, and locons, corresponding to the propagating, diffusion, and localized modes, respectively. The relative contribution of each of these modes dictates the thermal conductivity of the material, including its magnitude and its dependence on sample size and temperature. In this article, we will review the fundamental principles and recent development regarding thermal transport in amorphous semiconductors.