  In the present article we introduce and study a class of topological
reflection spaces that we call Kac-Moody symmetric spaces. These generalize
Riemannian symmetric spaces of non-compact type. We observe that in a
non-spherical Kac-Moody symmetric space there exist pairs of points that do not
lie on a common geodesic; however, any two points can be connected by a chain
of geodesic segments. We moreover classify maximal flats in Kac-Moody symmetric
spaces and study their intersection patterns, leading to a classification of
global and local automorphisms. Unlike Riemannian symmetric spaces,
non-spherical non-affine irreducible Kac-Moody symmetric spaces also admit an
invariant causal structure. For causal and anti-causal geodesic rays with
respect to this structure we find a notion of asymptoticity, which allows us to
define a future and past boundary of such Kac-Moody symmetric space. We show
that these boundaries carry a natural polyhedral structure and are cellularly
isomorphic to the halves of the geometric realization of the twin buildings of
the underlying split real Kac-Moody group. We also show that every automorphism
of the symmetric space is uniquely determined by the induced cellular
automorphism of the future and past boundary. The invariant causal structure on
a non-spherical non-affine irreducible Kac-Moody symmetric space gives rise to
an invariant pre-order on the underlying space, and thus to a subsemigroup of
the Kac-Moody group. We conclude that while in some aspects Kac-Moody symmetric
spaces closely resemble Riemannian symmetric spaces, in other aspects they
behave similarly to ordered affine hovels, their non-Archimedean cousins.
