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Vaughan Jones' theory of subfactors has lead to the discovery of many new quantum symmetries that produce interesting quantum invariants of knots and 3-manifolds. Moroever, subfactor techniques, such as planar algebras or commuting squares, can be used to construct exotic quantum channels with interesting commutativity properties. These constructions entail new insights into Jones' index problem. I will discuss some recent works on subfactors and quantum symmetries, partially joint with Julio Caceres and Junhwi Lim.