We study the deformation theory of nearly G_2 manifolds. These are seven dimensional manifolds admitting real Killing spinors. We show that the infinitesimal deformations of nearly G_2 structures are obstructed in general. Explicitly, we prove that the infinitesimal deformations of the homogeneous nearly G_2 structure on the Aloff--Wallach space are all obstructed to second order. We also completely describe the cohomology of nearly G_2 manifolds. The talk is based on a joint work with Shubham Dwivedi (HU, Berlin).