Bed particle saltation in turbulent wall-shear flow remains an intriguing phenomenon in applied hydrodynamics. In this review, we report the current state of the art of bed particle saltation in turbulent wall-shear flow, highlighting the physical characteristics of bed particle saltation and its mathematical modelling. A critical appraisal of the mechanics of bed particle saltation is presented thorough ample experimental evidence. The salient features of bed particle saltation, encompassing the saltation height, saltation length, particle velocity, saltation duration, particle collision with the bed, particle rotation, particle resting time and particle re-entrainment, are thoroughly discussed. Both the deterministic and computational fluid dynamics approaches in modelling bed particle saltation are summarized, and the subtle role of the hydrodynamic forces is elaborated. The estimation of bedload flux in a fluvial environment, emanating from the mathematical modelling of bed particle saltation, is delineated using different modelling approaches. Finally, the challenges in modelling bed particle saltation are highlighted, and a new look at bed particle saltation is furnished. © 2019 The Author(s) Published by the Royal Society. All rights reserved.