Concrete is one of the most widely used building materials since the nineteenth century. The manufacture of concrete includes the binder (cement), aggregates, water and possible additives. Although very versatile and durable, in the early 1900s, it was recognized that concrete can deteriorate and in consequence, compromise the durability and good functioning of the structures. From the many different damage mechanisms that can originate the deterioration of concrete, alkali–silica reaction (ASR) is the one that involves the aggregates. Aggregates constitute about three-quarter of the volume of concrete, and therefore their physical and chemical properties need to be correctly assessed before their use in concrete. Since the 1940s, considerable research has been developed to determine which components of the rocks and minerals contribute to the chemical reaction involved in this process of deterioration. However, a lot still remains to be understood. In the present article, an introduction to the subject is made, focusing mainly on the mechanisms and on the manifestations of the ASR.