  We review the recently discovered interplay between chaos and symmetry in the
general inhomogeneous solution of many string-related Einstein-matter systems
in the vicinity of a cosmological singularity. The
Belinsky-Khalatnikov-Lifshitz-type chaotic behaviour is found, for many
Einstein-matter models (notably those related to the low-energy limit of
superstring theory and M-theory), to be connected with certain
(infinite-dimensional) hyperbolic Kac-Moody algebras. In particular, the
billiard chambers describing the asymptotic cosmological behaviour of pure
Einstein gravity in spacetime dimension d+1, or the metric-three-form system of
11-dimensional supergravity, are found to be identical to the Weyl chambers of
the Lorentzian Kac-Moody algebras AE_d, or E_{10}, respectively. This suggests
that these Kac-Moody algebras are hidden symmetries of the corresponding
models. There even exists some evidence of a hidden equivalence between the
general solution of the Einstein-three-form system and a null geodesic in the
infinite dimensional coset space E_{10} / K(E_{10}), where K(E_{10}) is the
maximal compact subgroup of E_{10}.
