  Geometric flows have proved to be a powerful geometric analysis tool, perhaps
most notably in the study of 3-manifold topology, the differentiable sphere
theorem, Hermitian-Yang-Mills connections and canonical Kaehler metrics. In the
context of G_2 geometry, there are several geometric flows which arise. Each
flow provides a potential means to study the geometry and topology associated
with a given class of G_2 structures. We will introduce these flows, and
describe some of the key known results and open problems in the field.
