Even though friction affects everyday life in many ways, it is still one of the biggest mysteries of physics. Friction is a truly multi-scale phenomenon with a large variety of processes acting at various length and time scales. In recent years, much attention was paid to the micro- and nano-scale properties of frictional interfaces in order to uncover the origins of friction. The structural aspects of friction at the meso- to macro-scales have, however, often been neglected. This thesis aims at demonstrating that these aspects are key to the frictional response of macroscopic systems and pursues therefore the objective of improving today's knowledge of the rupture-like propagation of slip fronts at frictional interfaces. The mechanics of frictional interfaces is studied with state-of-the-art dynamic finite-element simulations of systems mimicking experimental set-ups. Two and three-dimensional simulations are conducted according to the nature of the studied phenomena. In addition, theoretical models based on fracture mechanics theory are developed and applied to confirm the numerical observations. These models provide insights on the underlying mechanisms of the slip front propagation and reveal the influence of various system, material, and interface parameters. The results presented in this thesis show that the applied numerical models reproduce quantitatively well experimental observations as reported in literature. The studied aspects of frictional slip include, among others, the propagation speed, the arrest position, and the effect of interface heterogeneity. Beyond confirming experimental observations, the simulations and theoretical models further reveal new features of the propagation and arrest of slip fronts. They show, for instance, that the speed of slip fronts depends on the propagation direction and that the arrest position of slip precursors is predictable with linear elastic fracture mechanics theory. Furthermore, simulations of slip fronts at heterogeneous interfaces uncover an interaction between the length scales of the slip front and the heterogeneous pattern.