  In this article, we summarize the results on symmetric conformal geometries.
We review the results following from the general theory of symmetric parabolic
geometries and prove several new results for symmetric conformal geometries. In
particular, we show that each symmetric conformal geometry is either locally
flat or covered by a pseudo-Riemannian symmetric space, where the covering is a
conformal map. We construct examples of locally flat symmetric conformal
geometries that are not pseudo-Riemannian symmetric spaces.
