SN 1987A appears to be a core-collapse supernova, which should result in a neutron star given the size of the original star. The neutrino data indicate that a compact object did form at the star’s core. However, since the supernova first became visible, astronomers have been searching for the collapsed core but have not detected it. The Hubble Space Telescope has taken images of the supernova regularly since August 1990, but, so far, the images have shown no evidence of a neutron star. A number of possibilities for the ‘missing’ neutron star are being considered. The first is that the neutron star is enshrouded in dense dust clouds so that it cannot be seen. Another is that a pulsar was formed, but with either an unusually large or small magnetic field. It is also possible that large amounts of material fell back on the neutron star, so that it further collapsed into a black hole. Neutron stars and black holes often give off light as material falls onto them. If there is a compact object in the supernova remnant, but no material to fall onto it, it would be very dim and could therefore avoid detection. Other scenarios have also been considered, such as whether the collapsed core became a quark star.