We describe the collapse behavior of remnants of neutron star mergers. A merger may form a black hole promptly or only on a longer time scale or possibly never. This distinction is highly relevant for the mass ejection, the conditions for short gamma-ray bursts and the character of postmerger gravitational wave emission. We argue that GW170817 likely did not result in a direct gravitational collapse. Based on these arguments one can derive a robust lower limit on neutron star radii, which nicely complements upper limits from current constraints on the tidal deformability. Moreover, we discuss that a future detection of postmerger gravitational wave emission can provide a direct measurement of neutron star radii and information on the dynamics of the merger remnant.