The effects of curing on the mechanical properties, chemical composition, microstructure and shrinkage of optimised alkali-activated concretes (AACs) based on ternary mixtures of fly ash (FA), blast-furnace slag (BFS) and Portland cement (PC) were compared. Heat treatment was found to accelerate the early-age strength development of both the PC concrete and the AAC. The long-term strength of AAC was not adversely affected by the heat treatment after 90 d of dry curing. Water curing slightly enhanced the ultimate long-term strength of non-heat-treated AAC specimens but had barely any effect on the heat-treated specimens. Conversely, the dry-cured PC specimens showed a significant decrease in long-term compressive strength. The ultimate drying shrinkage of the PC concrete was lower compared with the AAC, independent of the type of applied curing. In the case of AAC, the drying shrinkage was significantly decreased by the application of heat treatment while water curing did not have any measurable effect. Conversely, the drying shrinkage of AAC cured at ambient temperatures was decreased with the application of water curing. Compared with the PC concrete, the microstructure of the AAC samples was denser and more homogeneous without visible microcracking of the binder matrix. The dominant phases were geopolymer and calcium silicate hydrate (C-S-H) gels intermixed with probably sodium and aluminium ions and crystalline inclusions of zeolitic hydroxysodalite. A large amount of unreacted FA and BFS was observed in the hardened binder matrix of the AAC specimens. At the same time, no anhydrous PC was observed, thus indicating its extensive dissolution and contribution to the formation of the modified C-S-H gel.