  Exploring the shape of point configurations has been a key driver in the
evolution of TDA (short for topological data analysis) since its infancy. This
survey illustrates the recent efforts to broaden these ideas to model spatial
interactions among multiple configurations, each distinguished by a color. It
describes advances in this area and prepares the ground for further exploration
by mentioning unresolved questions and promising research avenues while
focusing on the overlap with discrete geometry.
