abstract: The 3D index is an invariant for cusped 3-manifolds introduced by Dimofte-Gaiotto-Gukov in 2011, which seems to contain a lot of information about the topology and geometry of the manifold. After a brief introduction, I'll describe our q-hypergeometric approach to study the behaviour of this invariant under Dehn filling. This is joint work with C. Hodgson and H. Rubinstein.