Nano-phononic crystals have attracted a great deal of research interest in the field of nanoscale thermal transport due to their unique coherent thermal transport behavior. So far, there have been many advances in the theory and simulation studies of coherent thermal transport in nanophononic crystals. In this paper, we summarize the state-of-the-art studies in this field from the perspective of coherent thermal transport at low temperatures, minimum thermal conductivity, Anderson localization, in various nanosystems, and in the frame of machine learning driven studies. Each part is specifically presented under different simulation methodologies, in which the background theories are also summarized. Accordingly, the controversies between different methodologies in describing wave-like/coherent and particle-like/incoherent thermal phonons are discussed. Various effects on coherent thermal transport are reviewed, including interface roughness, mass disorder, structural randomness, aperiodic ordering, and temperature effect. Finally, an outlook on the future research on coherent thermal transport in nano-phononic crystals is given. This overview provides fundamental and advanced knowledge to understand the coherent thermal transport in nano-phononic crystals, which will be beneficial to the further understanding of the physical picture of thermal phonons and heat transfer related applications.