  We review the often forgotten fact that gravitation theories invariant under
local de Sitter, anti-de Sitter or Poincare transformations can be constructed
in all odd dimensions. These theories belong to the Chern-Simons family and are
particular cases of the so-called Lovelock gravities, constructed as the
dimensional continuations of the lower dimensional Euler classes. The
supersymmetric extensions of these theories exist for the AdS and Poincare
groups, and the fields are components of a single connection for the
corresponding Lie algebras. In 11 dimensions these supersymmetric theories are
gauge theories for the osp(1|32) and the M algebra, respectively. The relation
between these new supergravities and the standard theories, as well as some of
their dynamical features are also discussed.
