Around 3-manifold groups

This text is an expanded version of the minicourse given at the session Winter Braids VIII. The goal is to present some basic properties of 3-manifold groups and to give an overview of some of the major progress made in their study this last decade. It is mostly of expository nature and does not intend to cover the subject. I thank the Winter Braids organizers for their invitation and their kind patience whilst these notes were completed, and the referee for his careful reading and his suggestions which greatly improved the exposition.