In geometric group theory, a classical aim is to study finitely generated groups by exploring the connections between their algebraic properties and the topological and geometric properties of spaces on which these groups act. In this talk, we introduce a different viewpoint for studying finitely generated groups, namely, profinite rigidity. A central question in this area is which group structures or properties can be detected through their finite quotients. We provide some background on this line of research and present recent developments in the area. We then present two recent results, one joint with Junseok Kim (Technion) and the other with Hyungryul Baik (KAIST).