In the light of one of the most common waste management issues in urban areas, namely the elimination of municipal solid waste (MSW; about 486 kg of the waste per capita were generated in the EU in 2017), this study discusses one technique as an outlet in the construction industry for the by-product of the waste’s incineration in energy recovery facilities (i.e., MSW incinerator bottom ash—MIBA). There have been some investigations on the use of MIBA as partial replacement of cement to be used in cementitious composites, such as concrete and mortars. However, the waste’s incorporation ratio is limited since further products of hydration may not be produced after a given replacement level and can lead to an unsustainable decline in performance. In order to maximize the incorporation of MIBA, some research studies have been conducted on the alkali activation of the waste as precursor. Thus, this study presents an extensive literature review of the most relevant investigations on the matter to understand the material’s applicability in construction. It analyses the performance of the alkali-activated MIBA as paste, mortar, and concrete from different perspectives. This literature review was made using search engines of several databases. In each database, the same search options were repeated using combinations of various representative keywords. Furthermore, several boundaries were made to find the most relevant studies for further inspection. The main findings of this review have shown that the chemical composition and reactivity of MIBA vary considerably, which may compromise performance comparison, standardization and commercialization. There are several factors that affect the performance of the material that need to be considered, e.g., type and content of precursor, alkaline activator, curing temperature and time, liquid to solid ratio, among others. MIBA-based alkali-activated materials (AAM) can be produced with a very wide range of compressive strength (0.3–160 MPa). The main factor affecting the performance of this precursor is the existence of metallic aluminum (Al), which leads to damaging expansive reactions and an increase in porosity due to hydrogen gas generation stemming from the reaction with the alkaline activator. Several approaches have been proposed to eliminate this issue. The most effective solution was found to be the removal of Al by means of eddy current electromagnetic separation.