A newly formed neutron star in a supernova finds itself in a dense environment, in which the gravitational energy of accreting matter can be lost to neutrinos. For the conditions in SN 1987A, ≲0.1M ⊙ may have fallen back onto the central neutron star on a timescale of hours after the explosion, after which the accretion rate is expected to drop sharply. Radiation is trapped in the flow until the mass accretion rate drops to 2×10-4 M ⊙ yr-1 at which point radiation can begin to escape from the shocked envelope at an Eddington limit luminosity. Between this neutrino limit and the Eddington limit, 3×10-8 M ⊙ yr-1, there are no steady, spherical solutions for neutron star accretion. SN 1987A should have reached the neutrino limit within a year of the explosion; the current lack of an Eddington luminosity can be attributed to black hole formation or to a clearing of the neutron star envelope. There is no evidence for newly formed neutron stars in supernovae. Radio supernovae, which were initially interpreted as pulsar activity, probably involve circumstellar interaction; SN 1993J shows especially good evidence for outer shock phenomena.