In today's quantum mechanics and quantum field theory, the observable signature of a symmetry is often sought in the form of a selection rule: a missing radiation frequency, a particle that does not decay in another one, a scattering process which fails to take place. The connection between selection rules and symmetries is effected thanks to the mathematical discipline of group theory. In the present paper, I will offer an overview of how the productive synergy between selection rules and group theory came to be. The first half of the work will be devoted to the emergence of the idea of spectroscopic selection rules in the context of the old quantum theory, showing how this notion was linked with an interpretive scheme of theoretical nature which, once combined with group theory, would bear many fruits. In the second part of the paper, I will focus on the actual encounter between selection rules and group theory, and on the person largely responsible for it: Eugene Wigner. I will attempt to reconstruct the path which led Wigner, of all people, to be the agent effecting this connection.