This talk will survey the classification of group actions on C*-algebras. One can often observe a rigid behavior of suitable classes of outer actions on nice C*-algebras, not unlike what is discussed in the mini-course by Stefaan Vaes. In contrast to the case of injective factors, however, the additional topological fine structure exhibited by simple nuclear C*-algebras makes the classification problem more subtle in general, requiring for example sophisticated tools from K-theory. Nevertheless, there are certain core ideas that are common to most results about classifying C*-dynamics, which will be illustrated by discussing the case of finite group actions with the Rokhlin property. In a way, this is the easiest possible abstract case to consider. If time permits, we will discuss further milestone results without proofs, with some emphasis on what the additional technical pitfalls and challenges are compared to the easy case of Rokhlin actions of finite groups.
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