The problem of mechanical contact is a truly multiscale one. Atomistic effects that violate continuum theory dominate the deformations of contacting asperities, while the interactions between distant asperities occur through long-range elasticity. This thesis concentrates on the numerical modelling of nanoscale frictional contact between crystalline metals by using both single-scale atomistic methods and improving concurrent multiscale methods. A novel approach to quantify frictional work and the energy associated with plastic activity in \md simulations is presented. In combination with a statistical criterion to determine the significance of simulation box size, microstructure and sliding rate effects on the frictional quantities such as the friction coefficient and stored plastic energies, the method is used in a large parametric molecular dynamics study of single-asperity nanoscratch on monocrystalline and polycrystalline aluminium substrates. Some fundamental differences in the friction mechanisms between monocrystalline and polycrystalline substrates are presented. The study shows the limitations of single-scale modelling and highlights the importance of developing appropriate multiscale methods for nanoscale plasticity. One such method is the Coupled Atomistics and Discrete Dislocations (CADD), which previously only existed for two-dimensional problems. A three-dimensional version of the CADD method is presented theoretically as well as a detailed practical road map for its efficient implementation. The foundations of three-dimensional CADD are presented using practical test cases. CADD avoids ghost forces at the coupling interfaces through displacement-coupling. I reveal that such displacement-coupling methods generally exhibit an inherent dynamic instability which makes them particularly ill suited for finite temperature calculations, despite their wide use. The instability is analysed in detail. Multiple remedies to manage it are discussed and a fundamental solution to the underlying problem is presented in the form of a new coupling method.