Since the discovery of the Jones polynomial in the 1980's, it is well-known that subfactors of von Neumann factors are intimately related to quantum topology. A subfactor is said to have infinite representation theory, if its standard representation generates infinitely many non-equivalent irreducibles. Such subfactors are quite hard to come by, and very few methods are known to produce interesting examples. I will highlight one such procedure, due to Vaughan Jones and myself. The construction yields new C$^*$-tensor categories and solutions of the quantum Yang-Baxter equation. If time allows, I will also talk about invariants for subfactors beyond the standard invariant.