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Macroscale friction behaviour originates from microscale asperity interactions. However, it is still not well-understood how the microscale asperity interactions determine the macroscale friction behaviour under different loading conditions. The current study aims to numerically investigate and reveal the friction behaviour and mechanism of sliding and rolling-sliding contacts, in particular, to quantitatively study the microscale asperity interactions and their contributions to overall friction behaviour. The following contributions have been made in this thesis. Firstly, an analytical model for the contact of rough surfaces was derived based on the essentials and the physical understanding of the contact phenomena, as presented in Chapter 4. The contact process of Gaussian random surfaces and fractal surfaces were studied and presented in terms of the real contact area, elastic load, plastic load, and plastic ratio. Secondly, an innovative friction prediction model was derived in Chapter 5, where the macroscale sliding friction was predicted from the combined result of the molecular and mechanical components of each individual asperity. Numerical results provide insight into the effect of surface roughness on the mechanical and molecular components of friction, that is, the mechanical component dominates the friction coefficient when the surface is rough, whilst the friction coefficient is mainly determined by the molecular component when the surface is relatively smooth. Furthermore, an optimal roughness value for minimising the friction coefficient is predicted. Thirdly, a numerical model for the friction prediction of rolling-sliding contact in mixed Elasto-hydrodynamic lubrication (EHL) was developed in Chapter 6, where the friction of mixed EHL was predicted by the combined result of lubricants fluid, boundary film and solid-to-solid frictions. Numerical results demonstrate that: 1) the friction is dominated by the solid-to-solid ploughing and adhesion friction in boundary lubrication regime, 2) in the mixed EHL regime, the overall friction coefficient shows a significant decreasing trend with the increase in velocity due to the decrease in solid-to-solid friction, and 3) the boundary film friction does not show a significant influence on the overall friction in both boundary and mixed lubrication regimes.