Given a finite set, the collection of partitions of this set forms a poset category under the coarsening relation. This category is directly related to a space of trees, which in turn has interesting connections to operads. But what if the finite set comes equipped with a group action? What is an “equivariant partition”? And what connection is there to equivariant trees? We will explore possible answers to these questions in this talk, based on joint work with J. Bergner, P. Bonventre, D. Chan, and M. Sarazola.