In recent years, applications of non-Newtonian fluids as lubricants have received great interest since the use of these non-Newtonian lubricants showed an increase in load carrying capacity and reduction in frictional force with the escalation in additives concentration. The demands of the present day industry rotating machinery includes high speed, compactness, light weight engines, high operating loads, high power transmission, high efficiency, and high performance of the engine. As a result of high speed machines, bearings are inclined to have excessive power loss and increasein oil temperature. The former reduces the efficiency of the engine and the latter causes the undesired changes in the lubricating oil. The plain journal bearings at high rotation speeds are subjected to instability like oil whirl and whip ruining the bearing and also the machine. Therefore, this poses a need to change in the bearing design. In the present paper, an attempt is made to briefly introduce the various non-linear models used and the different approaches that have been carried out by the researches in the past few years to improve and achieve the stability of journal bearing along with enhanced performances and characteristics.