Associative submanifolds are certain 3-dimensional manifolds in 7-dimensional manifolds. They are calibrated, and therefore minimal surfaces, and there is a research programme that attempts to count them in order to define numerical invariants of manifolds, similar to Gromov-Witten invariants. However, not many examples of associative submanifolds are known, which is one of the difficulties in working out the details of this programme. In the talk I will explain how to construct some dozens of associatives whose existence had previously been predicted by physicists.