In the 1980s new invariants of links and 3-manifolds were put forward by Jones, Reshetikhin–Turaev, and others.  Witten’s approach was based on quantum field theory, and it spurred decades of developments in the mathematics of topological field theory.  Building on that foundation, Claudia Scheimbauer, Constantin Teleman, and I recently used the cobordism hypothesis to construct the relevant 3-dimensional topological field theories (arXiv:2601.05518).  I will review these developments and discuss the new work.