Behavior of a system with friction at the interface is inherently nonlinear. Nonlinearities associated to interfacial mechanics primarily are the onset of sliding and energy dissipation. Firstly, to understand friction a finite element model is used to simulate sliding inception of a rigid flat on a deformable sphere under combined normal and tangential loading. Sliding inception is treated as the loss of tangential contact stiffness under combined effects of plasticity, crack propagation and interfacial slip. For fully adhered contact condition, plasticity is shown to be the dominant failure mechanism. Interplay of plasticity and interfacial slip is found to govern the onset of sliding for higher local friction coefficients. Furthermore, the single asperity results are incorporated in a statistical model of nominally flat rough surfaces under combined normal and tangential loading to investigate the stochastic effects due to surface roughness and material property uncertainties. The results show that the static coefficient of friction strongly depends on the normal load, material properties, local interfacial strength (adhesive friction component) and roughness parameters. The proposed model can be used as a measure for uncertainties that significantly influence the static friction coefficient. To investigate energy dissipation at an interface, a low cyclic tangential load is applied to obtain the hysteresis loops for the spherical model. The energy dissipation is studied under the influence of elastic mismatch, plasticity and varying phase difference between tangential and normal load. The energy losses are then correlated against the maximum tangential load as a power-law where the exponents show the degree of nonlinearity. Inducing a phase difference of 90 degrees between normal and tangential loads lead power-law exponents closer to 2; i.e., quadratic dependence of energy dissipation on tangential force. The results from the asperity scale are once again extended to the rough surface scale to study the effects of roughness parameters. The power-law exponent is found to be largely independent of roughness parameters as asperity density, asperity height distribution and fractal dimension. Achieving power-law exponents closer to 2 can be viewed as a first step in devising a predictive interfacial damping for frictional contacts.