Linear representations of posets arise in several areas of mathematics, including Morse theory and topological data analysis. Persistence studies the algebraic properties of these representations and their behavior under perturbations in the interleaving distance. When the indexing poset is not totally ordered, the category of such representations is usually of wild type, so a lot of work has been devoted to the study of isomorphism-invariants of poset representations. I will give an overview of recent results, both positive and negative, in particular concerning group-valued invariants.