Friction and wear occur at every interface between solid materials. In the design of mechanical devices, it is desirable to be able to quantify and control the amount of friction and wear, as well as predict their evolution with time. ``Tribology'' is the science looking at interactive surfaces in relative motion, which involves many phenomena such as friction, wear, lubrication, and corrosion. Phenomenological models can be used to make predictions on tribological behaviors (the Coulomb's friction law, for example), but they must be tuned with experimental values, that are not directly available when developing novel materials or surface treatments. From a scientific point of view, these models give little to no insight into the mechanisms involved. This thesis aims to enhance the current understanding of dry friction and wear at a more fundamental level. All surfaces are rough over a range of length scales, whether they are man-made or natural. When two rough surfaces are put into contact with each other, only a fraction of the total apparent area is actually in contact. To study friction and wear in this context, we must go down at the scale of the smallest asperities of the rough surfaces, where contact happens. The main goal of this thesis is to acquire an understanding of adhesive wear from the nanoscale, and establish a link with the larger scales. To do so, we start by working at the asperity scale, using analytical theories and molecular dynamics simulations to investigate the wear of several interacting micro-contacts. The elastic interactions enable the emergence of a wear regime featuring large wear volumes that are not observed when considering the micro-contacts in an isolated manner, predicting the existence of a severe wear regime. The emergence of severe wear is also found with rough contacts at a larger scale, solved using the boundary element method. To upscale the dynamical nanoscale processes of friction and wear uncovered during this thesis, a coarse-grained discrete element model was formulated. This model is capable of reproducing the adhesive wear mechanisms observed with molecular dynamics, and it can handle more complex situations involving the creation of third-body particles and a third-body layer. The temporal evolution of tribological interfaces is investigated using this model and with the help of physical experiments. We found that the wear process starts with the formation of small wear particles, whose size is dictated by the material properties. The particles grow and merge into a third-body layer, responsible for the macroscopic roughness and providing the sliding resistance. Finally, using some of the knowledge earned along the way, a practical case was investigated. The tribological influence of an oxide layer on silicon samples was assessed using experiments and numerical simulations. We found that the presence of the oxide layer reduces the wear rate of the protected piece, but increases the friction coefficient. While this thesis was restricted to the study of unlubricated adhesive wear, its founding principles and the developed tools could be used to look at abrasion and lubricated contacts.