  This paper is a review of current developments in the study of moduli spaces
of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional
holonomy group G2. Although they are odd-dimensional, in many ways they can be
considered as an analogue of Calabi-Yau manifolds in 7 dimensions. They play an
important role in physics as natural candidates for supersymmetric vacuum
solutions of M-theory compactifications. Despite the physical motivation, many
of the results are of purely mathematical interest. Here we cover the basics of
G2 manifolds, local deformation theory of G2 structures and the local geometry
of the moduli spaces of G2 structures.
