The modular representation theory of a finite group G concerns the study of finitely generated modules over the group algebra kG, where k is a field of positive characteristic. Such modules can be organised using the concepts of relative projectivity, vertex and source. Basic results of Green and Higman along these lines constitute fundamentals upon which the subject is built. A profinite group is the inverse limit of an inverse system of finite groups. In this talk we will see how many of the foundational results of modular representation theory of finite groups pass through this inverse system, to the limit.