All mechanical systems, naturally occurring or human-produced, are subjected to friction and wear at the interface of solid constituents. Large portions of energy dissipation and loss of material, in every-day life and industrial applications alike, are due to friction and wear. Mitigating their effects could save between 1\% and 2\% of the GDP of a developed country. Some systems governed by friction and wear can have an even more important bearing on human lives, such as earthquakes nucleating from the sliding of tectonic faults. Despite the tremendous impact of tribological phenomena on society, their understanding has remained empirical, and to this day no predictive model has emerged. Interface processes such as friction and wear are difficult to investigate because of the large number of underlying physical phenomena (e.g. adhesion, fracture, etc.) and the difficulty of observing them at contact interfaces. Although research endeavors into friction and wear have not produced predictive models, they have identified key components of tribological systems necessary to build such models. Central among them is the idea that solids may not be in contact across their apparent interface area, but instead a much smaller "true contact area." This true contact area is the result of the surfaces in contact being inevitably rough. In addition, contact pressures on roughness peaks are expected to cause plastic flow of material, drastically changing the properties of the contact interface, and the role it plays in tribological processes. Therefore, the aim of this PhD thesis is to develop tools for the modeling of elastic-plastic rough contact interfaces, and to study the applicability of knowledge of the contact state to the modeling of interface phenomena. The first part of this objective is the development of a novel computational approach to volume integral methods, which are used to solve elastic-plastic rough surface contact. Volume integral methods have the advantage over the finite-element method in that they can represent exactly elastic constitutive behavior and semi-infinite bodies, which are commonly used in rough contact applications. This thesis develops a new fundamental solution used in a volume integral approach, which drastically improves computation times and required memory over previous approaches. Derived directly in the Fourier domain, this fundamental solution makes optimal use of the fast-Fourier transform while retaining the advantages of classical volume integral methods. In the second part, this numerical approach is used to study the so called "Archard's wear coefficient", and to up-scale known micro-scale adhesive wear mechanisms to the macro-scale via rough contact simulations. These show that wear is an emergent process dependent on the interaction of micro-scale mechanisms: they demonstrate the role of plastic deformations in the crack nucleation process, and the necessity to look beyond the true contact area to understand tribological phenomena. While this thesis remains quite fundamental, the tools and codes developed can be used outside the realm of elastic-plastic contact, and the up-scaling approach to wear that we have established is a first step towards predictive models.