The Brauer and partition algebras, introduced by Brauer and Martin respectively, are examples of diagram algebras. The representation theory of both of these over a field of characteristic zero is well understood.
In this talk, I will recall the block structure of the Brauer and partition algebras in characteristic zero in terms of the action of a reflection group on the set of simple modules. I will then give a description of the blocks in positive characteristic by using the corresponding affine reflection group (for the partition algebra, this is joint work with C. Bowman and M. De Visscher). Finally I will show that by restricting our attention to specific families of these algebras, we can in fact obtain the entire decomposition matrix.