Nuclear dimension of simple $$\mathrm {C}^*$$-algebras

We compute the nuclear dimension of separable, simple, unital, nuclear, $${\mathcal {Z}}$$ -stable $$\mathrm {C}^*$$ -algebras. This makes classification accessible from $${\mathcal {Z}}$$ -stability and in particular brings large classes of $$\mathrm {C}^*$$ -algebras associated to free and minimal actions of amenable groups on finite dimensional spaces within the scope of the Elliott classification programme.