The alkali-silica reaction (ASR) is one of the most common causes of internal concrete degradation. This chemical reaction occurs between the amorphous silica contained inside the aggregates, and the alkalis of the cement pore solution. During the reaction hydrophilic silica gel forms, which starts swelling as it absorbs water. This induces internal stresses in the concrete, which in turn cause macroscopic expansion and cracking. Due to its deleterious effects on the mechanical properties of concrete, the ASR is more commonly known as concrete cancer. The speed of the chemical degradation process of ASR is slow and, thus, the consequences in an affected structure often become visible only after many service years. The need to assess the influence of the ASR-induced degradation process on the safety and serviceability of affected concrete structures has led to intensive research activities over the last decades. Both experimental and modeling studies, have provided fundamental insights on the physics of ASR at the meso-scale of concrete. At this scale concrete is typically described as a heterogeneous material, consisting of aggregates embedded in the cement paste. It is, however, not yet well understood how the mesoscopic damage evolution influences the overall material behavior of concrete at the macro-scale, i.e. the structural scale. In the present thesis a numerical framework for ASR is developed, which aims at providing answers regarding the link between the mesoscopic and macroscopic consequences of ASR. For this purpose an ASR meso-scale model is implemented in an open-source finite element library. This numerical development makes the execution of high-performance computing simulations possible, in which the complex ASR-induced crack networks can be captured with an unprecedented level of detail. Moreover, large sets of parametric studies are carried out in order to identify the main influencing numerical and physical parameters of the model. A multi-scale finite element approach is, subsequently, applied in order to up-scale the mesoscopic material response of ASR-affected concrete. This strategy allows to conduct simulations of the mechanical consequences of ASR in large concrete structures, in which the material behavior of concrete is directly governed by the physics of ASR occurring at the meso-scale.