Alkali-silica reaction occurs in concrete between the alkalis contained in the pore solution and silica in the aggregates. Generation of ASR products gives rise to the internal pressures that cause expansion and cracking. Due to its deleterious effect on concrete, ASR poses a major threat to the safety and operability of the concrete infrastructure worldwide. Recent experimental advances obtained in the scope of the multi-disciplinary Sinergia project entitled ``Alkali-silica reaction in concrete'' of Swiss research institutes shed new light on ASR. Being part of Sinergia, the research conducted in the scope of the present thesis had a goal to fill in the knowledge gap on the ASR mechanics. Therefore, analytical and numerical models facilitated by the novel experimental data have been developed. One of the Sinergia experimental studies showed that the initial ASR products accumulate between the crystal grains of aggregates. We are using this knowledge together with an estimate of the volumetric increase of a typical ASR product to evaluate the crack-growing potential of a single region filled with ASR products. This is done by employing a semi-analytical model of an expanding inclusion of nanometre-size encircled by a disk-shaped crack. The role of the expansion value and the inclusion's size and shape on the resulting crack length is investigated. The analytical findings are confirmed by a finite element model. Another experimental Sinergia study produced a time-series of X-ray tomograms of the ASR-affected concrete, which resolved the evolution of the deformation field, the crack growth and the accumulation of ASR products. This unique set of data is used in the current thesis to study the growth of ASR-crack networks and their role in the macroscopic behaviour of concrete. A novel cohesive elements-based meso-scale model capable of predicting the stable growth of numerous cracks is developed. Several hypotheses on the ASR-loading and cracking mechanisms are proposed and tested by including them in the model. Statistical comparison of the numerical and experimental crack networks provide new insights into ASR-cracking physics. The continuous-damage approach is adopted to improve the efficiency and stability of the meso-scale model. The physics of the model is enriched by accounting for the orthotropic behaviour of damaged elements and the self-contact in cracks. This development allows reproduction of the macroscopic expansion of the concrete samples under substantial uniaxial load, which was not feasible by the earlier isotropic-damage models. Moreover, the role of creep on the ASR in concrete is investigated by combining viscoelasticity with strain-softening. The last subject treated in this thesis is the macroscopic behaviour of ASR-affected structures. A computational multi-scale model of concrete is developed, validated and used to investigate the long-term behaviour of a real ASR-affected dam. The latter was facilitated by the availability of actual field measurements. This approach combines the meso-scale model with the orthotropic damage and the macro-scale model of the dam. The model allows us to relate the macroscopic expansion of concrete to its state at the meso-scale, which comprises the crack network, its openings and orientations, and expansions of individual ASR sites. Coupling of the mechanical model with the transient heat analysis permits to evaluate the role of temperature variations on the ASR expansion.