The development of new, sustainable, low-CO₂ construction materials is essential if the global construction industry is to reduce the environmental footprint of its activities, which is incurred particularly through the production of Portland cement. One type of non-Portland cement that is attracting particular attention is based on alkali-aluminosilicate chemistry, including the class of binders that have become known as geopolymers. These materials offer technical properties comparable to those of Portland cement, but with a much lower CO₂ footprint and with the potential for performance advantages over traditional cements in certain niche applications. This review discusses the synthesis of alkali-activated binders from blast furnace slag, calcined clay (metakaolin), and fly ash, including analysis of the chemical reaction mechanisms and binder phase assemblages that control the early-age and hardened properties of these materials, in particular initial setting and long-term durability. Perspectives for future research developments are also explored.