  We study `hilltop' inflation, in which inflation takes place near a maximum
of the potential. Viewed as a model of inflation after the observable Universe
leaves the horizon (observable inflation) hilltop inflation is rather generic.
If the potential steepens monotonically, observable hilltop inflation gives a
tiny tensor fraction (r< 0.002). The usual F- and D-term models may easily be
transmuted to hilltop models by Planck-suppressed terms, making them more
natural. The only commonly-considered model of observable inflation which is
definitely not hilltop is tree-level hybrid inflation. Viewed instead as an
initial condition, we explain that hilltop inflation is more generic than seems
to have been previously recognized, adding thereby to the credibility of the
idea that eternal inflation provides the pre-inflationary initial condition.
