Oppermann and Thomas introduced the $(d + 2)$-angulated cluster category to generalise the classical cluster category to higher homological algebra. A great difficulty that arises in these categories is that cluster-tilting objects are no longer mutable at every summand, in contrast to the classical setting. In this talk we give two new ways of understanding mutability in these higher cluster categories: one from an algebraic perspective, and the other from a combinatorial perspective for the particular case of the higher Auslander algebras of type $A$.