Continuing interest in energy conservation and friction reduction, driven primarily by environmental concerns, provides opportunities to develop energy saving lubricants. The greatest potential energy savings come from reductions in hydrodynamic friction as typified by main and connecting rod journal bearings in automotive engines. The main approach to minimise friction losses in these bearings is to reduce the lubricant viscosity. However, this approach will inevitably reduce oil film thickness and impose even higher stresses on the lubricant. The problem is compounded by the use of multigrade oils, which contain relatively high molecular weight polymeric components, and exhibit both temporary and permanent shear thinning. Thus these lubricants exhibit non-Newtonian flow behaviour under the extreme conditions imposed by engine bearings. One of the fascinating, largely unresolved, questions in Tribology concerns the effect of non-Newtonian lubricant behaviour on lubrication characteristics and bearing performance. To model the performance of bearing-lubricant systems requires a knowledge of the rheology of multigrade lubricants combined with a method of estimating the bearing kinematics and dynamics involved for operation under in-service conditions. In a collaborative project involving the University of Wales Institute of Non-Newtonian Fluid Mechanics at Aberystwyth and Shell Research and Technology Centre, Thornton, UK this problem has been elucidated.This paper presents an overview of the newly developed sophisticated numerical methods to model journal bearings. It will also demonstrate the importance of taking proper consideration of non - Newtonian lubricant rheology into account for applicability to engine journal bearings.