  The final evolution of stars in the mass range 70 - 140 solar masses is
explored. Depending upon their mass loss history and rotation rates, these
stars will end their lives as pulsational pair-instability supernovae producing
a great variety of observational transients with total durations ranging from
weeks to millennia and luminosities from 10$^{41}$ to over 10$^{44}$ erg
s$^{-1}$. No non-rotating model radiates more than $5 \times 10^{50}$ erg of
light or has a kinetic energy exceeding $5 \times 10^{51}$ erg, but greater
energies are possible, in principle, in magnetar-powered explosions which are
explored. Many events resemble Type Ibn, Icn, and IIn supernovae, and some
potential observational counterparts are mentioned. Some PPISN can exist in a
dormant state for extended periods, producing explosions millennia after their
first violent pulse. These dormant supernovae contain bright Wolf-Rayet stars,
possibly embedded in bright x-ray and radio sources. The relevance of PPISN to
supernova impostors like Eta Carinae, to super-luminous supernovae, and to
sources of gravitational radiation is discussed. No black holes between 52 and
133 solar masses are expected from stellar evolution in close binaries.
