In recent decades, geopolymer concrete has often been viewed as an alternative to traditional concrete. Although its comparatively lower production of greenhouse gas emissions during a lifecycle is usually mentioned at the top of the list of benefits, the possibility of using various waste materials in its production is a clear advantage as well. This literature review summarizes and analyses the existing information on the different available construction wastes for the production of geopolymer and foamed geopolymer concrete and analyzes the curing conditions, constituents in the aluminosilicate precursor, mechanical properties, and the activator type. As part of the literature review, the use of autoclaved aerated concrete and brick wastes has been evaluated. Autoclaved concrete has been chosen because it is a typical low-strength, cement-based construction material and demolition waste that is currently disposed of in landfills, making it quite a challenge for direct use as a supplementary cementitious material. On the other hand, brick waste, one of the most common construction wastes, can be feasibly used in the form of brick dust. This literature review uses data from randomly selected studies.