  This article is a report on the status of the problem of classifying the
irriducibly acting subgroups of GL(n,R) that can appear as the holonomy of a
torsion-free affine connection. In particular, it contains an account of the
completion of the classification of these groups by Chi, Merkulov, and
Schwachhofer as well as of the exterior differential systems analysis that
shows that all of these groups do, in fact, occur. Some discussion of the
results of Joyce on the existence of compact examples with holonomy G_2 or
Spin(7) is also included.
