“Microstate geometries” are a class of solutions to a generalisation of Einstein’s general relativity, speculatively linked to black holes, and possessing some unusual geometric features. In this talk I will present several results concerning the behaviour of linear waves on these geometries, which are linked to issues of (in)stability. In particular, I will show that the energy of waves is uniformly bounded, despite heuristic arguments for the “Friedman instability”. I will also show that these geometries are able to “trap” waves for an exceedingly long time, leading to sub-logarithmic decay rates. Finally, I will show that the energy of waves can only be bounded in terms of a higher order quantity and not in terms of the energy itself.