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.