I will explain how one can develop a dynamical version of some of the theory surrounding the Toms-Winter conjecture for simple separable nuclear C*-algebras. In particular, I will introduce a notion of almost finiteness for group actions on compact spaces as an analogue of both hyperfiniteness in the measure-preserving setting and of $/mathcal{Z}$-stability in the C*-algebra setting. This generalizes Matui's concept of the same name from the zero-dimensional context and is related todynamical comparison in the same way that $/mathcal{Z}$-stability is related to strict comparison in the Toms-Winter context. For free minimal actions of countably infinite groups on compact metrizable spaces the property of almost finiteness implies that the crossed product is $/mathcal{Z}$-stable, which leads to new examples of classifiable crossed products.  

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