Geopolymers have been a frequently studied topic during the last decades due to waste materials utilization, low energy demands, and low carbon dioxide emissions related to their production, which makes them very attractive within the current environmental trends. However, the original idea to use them as a concrete replacement showed to be unattainable in the nearest future, so other alternatives of geopolymers applications are being sought that could exploit the efforts spent and research progress made so far. This review paper summarizes the recent progress in the field of directly foamed geopolymers, as one of the alternatives, focusing on the material base, foaming and stabilization processes, and assessments of selected material parameters, as related to raw materials used and treatment techniques applied. As the main result, several gaps and challenges are identified that deserve more attention and deeper investigations, which can help to move the geopolymer foams closer towards their regular application in civil engineering. A detailed knowledge of hygric parameters and their influence on thermal properties, long-term performance analyses in real-world applications, or extension of the material base to achieve environmental more friendly solutions represent the most topical issues that are supposed to be addressed.