  We develop a framework that facilitates the study of the causal structure of
spacetimes with a causally preferred foliation. Such spacetimes may arise as
solutions of Lorentz-violating theories, e.g. Horava gravity. Our framework
allows us to rigorously define concepts such as black/white holes and to
formalize the notion of a `universal horizon', that has been previously
introduced in the simpler setting of static and spherically symmetric
geometries. We also touch upon the issue of development and prove that
universal horizons are Cauchy horizons when evolution depends on boundary data
or asymptotic conditions. We establish a local characterisation of universal
horizons in stationary configurations. Finally, under the additional assumption
of axisymmetry, we examine under which conditions these horizons are cloaked by
Killing horizons, which can act like usual event horizons for low-energy
excitations.
