In the lubricated pipe flow (LPF) of heavy oils, a water annulus acts as a lubricant and separates the viscous oil from the pipe wall. The steady state position of the annular water layer is in the high shear region. Significantly, lower pumping energy input is required than if the viscous oil was transported alone. An important challenge to the general application of LPF technology is the lack of a reliable model to predict frictional pressure losses. Although a number of models have been proposed to date, most of these models are highly system specific. Developing a reliable model to predict pressure losses in LPF is an open challenge to the research community. The current chapter introduces the concept of water lubrication in transporting heavy oils and discusses the methodologies available for modeling the pressure drops. It also includes brief descriptions of most important pressure loss models, their limitations, and the scope of future works.