The construction of coronas (i.e. boundaries at infinity) of combable spaces has been an open problem for quite a while. In this talk, I will present a very conceptual construction of such coronas under a convincing new additional assumption on the combing, called properness. Under two further additional conditions, coherence and expandingness, the compactification of a Rips complex construction by this corona can be shown to be contractible. This yields applications to isomorphism conjectures and dimension estimates for groups. This is joint work with Alexander Engel, arXiv:1711.06836.