I will discuss black holes in the context of Einstein–aether and khronometric gravity — two closely related alternative theories of gravity that allow violations of local Lorentz invariance. Since these theories admit faster-than-light propagation, metric horizons are generically permeable and it is not clear whether proper black holes can exist; surprisingly, in some cases they do, thanks to the appearance of a new kind of “universal” horizon. I will review past and recent results on the topic, with a particular emphasis on the difficulty of finding rotating solutions.