  For almost thirty years, mode-coupling theory has been the most widely
discussed and used but also the most controversial theory of the glass
transition. In this paper we briefly review the reasons for both its popularity
and its controversy. We emphasize the need for the development of approaches
that would be able to evaluate corrections to and extensions of the existing
(standard) mode-coupling theory. Next, we review our diagrammatic formulation
of the dynamics of interacting Brownian particles. We show that within this
approach the standard mode-coupling theory can be derived in a very simple way.
Finally, we use our diagrammatic approach to calculate two corrections to the
mode-coupling theory's expression for the so-called irreducible memory
function. These corrections involve re-summations of well defined classes of
non-mode-coupling diagrams.
