  Quasi-static systems are an important concept in thermodynamics: they are
dynamic but close enough to equilibrium that many properties of equilibrium
systems still hold. Slowly evolving horizons are the corresponding concept for
quasilocally defined black holes: they are "nearly isolated" future outer
trapping horizons. This article reviews the definition and properties of these
objects including both their mechanics and the role that they play in the
fluid-gravity correspondence. It also introduces a new property: there is an
event horizon candidate in close proximity to any slowly evolving horizon.
