This paper reviews numerical studies on the effect of expansion and damage due to alkali-silica reaction (ASR) on the mechanical performance of concrete and reinforced concrete at the structural scale level. Previous research on model development that has focused on the performance of RC members or structures is collected and summarized based on how they operationalize expansion progress. The models can be divided into three categories: models that receive the target expansion amount as an input value, models that use expansion curves, and models that calculate the increase in free expansion by considering the kinetic process of ASR. The aim of the model development can be related to either the deformation of the member or the load capacity for static or dynamic load actions. Expansion transfer under confined conditions is characteristic of the ASR problem, and the methods to model expansion transfer are accordingly summarized. Various considerations concerning the effect of ASR expansion and associated damage on the concrete constitutive laws are also studied. Expansion transfer under multi-axial stress states can be accurately reproduced by the modeling of expansion redistribution and volumetric expansion reduction under stress conditions. There are diverse methods to model the resultant deterioration of mechanical properties, but the primary method is by reducing the strength and elastic modulus according to empirically determined relationships. The ideal modeling approach is still under discussion because the effect of the anisotropic cracking state on the anisotropic mechanical response still requires further study. Finally, current problems of assessment of ASR-damaged concrete structures were discussed, and the significance of the causal correlation between macroscopic expansion behavior and microscale factors was suggested.