The sliced and max sliced Wasserstein metrics were originally proposed as a way to use 1D transport to speed up computation of the usual optimal transport metrics defined on spaces of probability measures. Some basic results are known about their metric structure, but not much is available in the way of a systematic study. In this talk, I will first discuss some further properties of these sliced metrics. Then, I will introduce a larger family of metric spaces into which these metrics can be embedded, which seem to have more desirable geometric properties. This talk is based on joint work with Asuka Takatsu.