The urgent need to reduce greenhouse gas emissions in combination with an increased use of sustainable energy resources have led to immense efforts on improving energy efficiency of mechanical systems. Consequently, modern machine elements are typically lubricated with low viscosity oils and designed to endure an increasingly high power density. This typically implies that the surfaces in contact are separated by thinner lubricant films that must carry higher loads. Thereby, in order to improve the durability and efficiency of future machine elements, an improved fundamental understanding of the predominant lubrication mechanisms must be achieved. This thesis concerns numerical simulation of non-conformal lubricated contacts where significant elastic deformations in combination with hydrodynamic effects govern the lubricating film formation, typically found in e.g., rolling element bearings, gears, and cam-follower systems. Such contacts relate to a lubrication regime known as elastohydrodynamic lubrication (EHL), which is often studied using simplifying assumptions due to its multiphysical nature. Typical simplifications of the EHL problem may include e.g., steady-state conditions, perfectly elastic surfaces, isothermal conditions, and Newtonian lubricant behaviour. However, such simplifications may be progressively relieved because of a continuously improved computer performance and the use of increasingly efficient numerical methods. In this work, time dependent simulations of EHL contacts are conducted with the purpose of improving the fundamental understanding of the predominant lubrication mechanisms. This is achieved by the development and utilisation of novel models and modelling techniques, specifically developed for the conducted investigations focusing on e.g., temperature, plastic deformation, surface roughness, and contact geometry. The developed models are all an extension of a full-system finite element modelling approach that was relatively recently introduced to the EHL community. Important findings from this work relate to the influence of transient fluctuations in EHL contacts, which occur due to both transient loads and moving surface roughness. It is shown that in the case of transient loading of a finite line EHL contact, a steady state assumption may overestimate the minimum film thickness and underestimate the maximum pressure over time due to the formation of lubricant waves travelling through the contact. Furthermore, thermal and non-Newtonian effects on viscosity may be necessary to consider in both qualitative and quantitative studies of roughness within the EHL contact, especially under sliding conditions and short wavelength roughness. Lastly, transient fluctuations related to the over-rolling of surface features are shown to potentially increase the pressure within the EHL contact to such an extent that plastic deformations of the contacting surfaces occur. The models established in this work may provide researchers and engineers with ways to improve their studies of transient EHL contacts. The salient findings from the conducted studies also open up for interesting directions that may be extended to potentially improve the lubrication theories currently in use and thereby improve the design of future machine elements that employ non-conformal contacts.