  The study of homological invariants such as Tor, Ext and local cohomology
modules constitutes an important direction in commutative algebra. Explicit
descriptions of these invariants are notoriously difficult to find and often
involve combining an array of techniques from other fields of mathematics. In
recent years tools from algebraic geometry and representation theory have been
successfully employed in order to shed some light on the structure of
homological invariants associated with determinantal rings. The goal of this
notes is to survey some of these results, focusing on examples in an attempt to
clarify some of the more technical statements.
