More than 60 years ago Richard Brauer developed the theory of representations of finite groups over arbitrary fields. It showed a strong connection between the representation theory of a finite group and that of its p-local subgroups, for p a prime. Many more such connections have been observed in the meantime, but most of these are still conjectural. Recently, a new reduction approach has offered the hope to solve all of these fundamental conjectures by using the classification of finite simple groups. In our talk we will try and explain the nature of these problems and will report on recent progress which might eventually lead to a solution of these long standing fundamental questions.