The amalgamation property of a class of structures is a well-known concept, important for building universal homogeneous models. We shall discuss its weakening, discovered by Ivanov in 1999, which turns out to be relevant in the study of so-called generic objects. Namely, a countable class of finitely generated structures with the joint embedding property has a generic limit if and only if it has the weak amalgamation property. The results come from joint works with A. Krawczyk, A. Kruckman, and A. Panagiotopoulos.