  This thesis explores two avenues into understanding the physics of black
holes and horizons beyond general relativity, via analogue models and Lorentz
violating theories. Analogue spacetimes have wildly different dynamics to
general relativity; this allows the possibility of non-Killing horizons in
stationary solutions. In the case of non-Killing horizons different definitions
of surface gravity are truly different quantities. This also has application to
modified theories of gravity, where there is no reason to expect all horizons
to be Killing horizons. In Lorentz violating theories, the situation becomes
even stranger, as Killing horizons are at best low energy barriers, but for
superluminal dispersion relations a true causal barrier, the universal horizon,
may be present. We investigate the nature of these universal horizons via a ray
tracing study, and delve into what happens near both the universal and Killing
horizons. From this study we determine the surface gravity of universal
horizons by the peeling properties of rays near the horizon and discuss
whether, and at what temperature these horizons radiate. Finally, we combine
our investigations of universal horizons and analogue spacetimes, and ask why
we have not seen a universal horizon in studies of analogue gravity.
