Phosphorene, a novel elemental 2D semiconductor, possesses fascinating chemical and physical properties which are distinctively different from other 2D materials. The rapidly growing applications of phosphorene in nano/optoelectronics and thermoelectrics call for comprehensive studies of thermal transport properties. In this Review, based on the theoretical and experimental progresses, the thermal transport properties of single-layer phosphorene, multilayer phosphorene (nanofilms), and bulk black phosphorus are summarized to give a general view of the overall thermal conductivity trend from single-layer to bulk form. The mechanism underlying the discrepancy in the reported thermal conductivity of phosphorene is discussed by reviewing the effect of different functionals and cutoff distances on the thermal transport evaluations. This Review then provides fundamental insight into the thermal transport in phosphorene by reviewing the role of resonant bonding in driving giant phonon anharmonicity and long-range interactions. In addition, the extrinsic thermal conductivity of phosphorene is reviewed by discussing the effects of strain and substrate, together with phosphorene based heterostructures and nanoribbons. This Review summarizes the progress of thermal transport in phosphorene from both theoretical calculations and experimental measurements, which would be of significance to the design and development of efficient phosphorene based nanoelectronics.