  Let $\mathscr{H}_n$ denote the Iwahori-Hecke algebra corresponding to the
symmetric group $\mathfrak{S}_n$. We set up a Green correspondence for
bimodules of these Hecke algebras, and a Brauer correspondence between their
blocks. We examine Specht modules for $\mathscr{H}_n$ and compute the vertices
of certain Specht modules, before using this to give a classification of the
vertices of blocks of $\mathscr{H}_n$ in any characteristic. Finally, we apply
this classification to resolve the Dipper-Du conjecture about the structure of
vertices of indecomposable $\mathscr{H}_n$-modules.
