Abstract: The profinite completion of a group is the inverse limit of all the finite quotient of the group. To what extent it determines the isomorphism type of the group itself was a group theoretic question, but the past decade has witnessed progress of the topic restricted to the class of 3-manifold groups. In this talk, I will give a general survey of what has been known and what remains unknown about 3-manifold groups and their profinite completions.
