The aim of this talk is to introduce equivariant versions of Ehrhart series of lattice polytopes and of Hilbert series of Stanley-Reisner rings of simplicial complexes. More precisely, we want to record how the action of a finite group affects the collections of lattice points or monomials that one usually "just" counts. Inspired by previous results by Betke-McMullen, Stembridge, Stapledon and Adams-Reiner, we will investigate which extra combinatorial features of the group action give rise to "nice" rational expressions of the equivariant Hilbert and Ehrhart series, and how the two are sometimes related. This is joint work with Emanuele Delucchi. A particularly well-behaved class of lattice polytopes is the one given by order polytopes of posets; if time permits, I will also mention a recent result about the gamma-effectiveness of order polytopes of graded posets. This is joint work with Akihiro Higashitani.