One natural starting point when studying a group is to investigate its finite quotients, and one might wonder how much these finite quotients can detect about the group in question. In particular, many have recently been interested in distinguishing fundamental groups of 3-manifolds using just their finite quotients. I will discuss some infinite families of Seifert fibered spaces whose fundamental groups can be shown to be (absolutely) profinitely rigid; each of these groups can be distinguished from all other finitely generated, residually finite groups by their finite quotients. I will also discuss how these 3-manifold groups can be used to create interesting new examples relating to Grothendieck’s problem on profinite completions and finite presentability. This is joint work with Martin Bridson and Alan Reid.