In fluvial sedimentology, bed sediment entrainment by streamflow has a decisive role in controlling several fluvial processes. Owing to its huge practical importance, the subject has been painstakingly explored for over a century. However, a detailed understanding of the mechanism of the bed sediment entrainment phenomenon achieved hitherto is far from complete. The central theme of bed sediment entrainment is occupied by the sediment entrainment threshold, which varies enormously in its qualitative definition, identification and quantification encompassing a broad range of spatiotemporal scales. This article presents the state of the science of the entrainment of non-cohesive bed sediments under a steady-unidirectional streamflow. It begins with the diverse definitions and representations of the entrainment threshold criterion from both qualitative and quantitative perspectives, scrutinising its suitability and ambit of applicability. Then, the effects of energetic factors that drive the entrainment threshold criterion are critically appraised. The indispensable mechanisms of bed sediment entrainment, including the theoretical background and modelling strategies, the role of turbulent bursting phenomenon and the phenomenological perspective into the origin of the scaling laws of sediment entrainment, are explained. Throughout the article, special emphasis is given to the strengths and weaknesses of the current state of the science. In addition, a deliberate attempt is made to invoke the thought-provoking ideas on the multifarious features of bed sediment entrainment. Finally, the innovative perspectives on the bed sediment entrainment are provided and the concluding remarks are made, elucidating the major challenges and suggesting the prospective ways to resolve them as a future scope of research. © 2018 The Authors. Sedimentology © 2018 International Association of Sedimentologists