  We review recent progress in understanding certain aspects of the
thermodynamics of black holes and other horizons. Our discussion centers on
various ``entropy bounds'' which have been proposed in the literature and on
the current understanding of how such bounds are {\it not} required for the
semi-classical consistency of black hole thermodynamics. Instead, consistency
under certain extreme circumstances is provided by two effects. The first is
simply the exponential enhancement of the rate at which a macrostate with large
entropy is emitted in any thermal process. The second is a new sense in which
the entropy of an ``object'' depends on the observer making the measurement, so
that observers crossing the horizon measure a different entropy flux across the
horizon than do observers remaining outside. In addition to the review, some
recent criticisms are addressed. In particular, additional arguments and
detailed numerical calculations showing the observer dependence of entropy are
presented in a simple model. This observer-dependence may have further
interesting implications for the thermodynamics of black holes.
