A group is called acyclic if its integral homology vanishes. I will describe how acyclic groups can be used to construct new models for familiar C*-algebras. In particular, I will give the first examples of torsion-free groups which are not C*-superrigid, that is I will describe a torsion-free group whose reduced group C*-algebra is isomorphic to the one of the free group on countably many generators. Moreover, I will discuss how the Jiang-Su algebra can be realized as a crossed product C*-algebra. If time permits, I will also consider other strongly self-absorbing algebras. This talk is based on joint work with Shanshan Hua and Raz Slutsky.