  This article reviews the properties and limitations associated with the
existence of particle, visual, and event horizons in cosmology in general and
in inflationary universes in particular, carefully distinguishing them from
`Hubble horizons'. It explores to what extent one might be able to probe
conditions beyond the visual horizon (which is close in size to the present
Hubble radius), thereby showing that visual horizons place major limits on what
are observationally testable aspects of a multiverse, if such exists. Indeed
these limits largely prevent us from observationally proving a multiverse
either does or does not exist. We emphasize that event horizons play no role at
all in observational cosmology, even in the multiverse context, despite some
claims to the contrary in the literature.
