The discovery of coalescing binary black holes by Advanced LIGO heralds the birth of a new field of research: gravitational wave (GW) astronomy. Coalescing neutron star (NS) binaries are among the new GW sources expected over the next few years. Maximizing the knowledge gained from this discovery will require identifying a coincident electromagnetic counterpart. One promising counterpart is an optical/IR flare, powered by the radioactive decay of neutron-rich elements synthesized in the merger ejecta (a so-called `kilonova'). Beyond providing a beacon to the GW chirp, kilonovae probe one of the dominant astrophysics sites for creating the heaviest elements in the Universe via rapid neutron capture (r-process) nucleosynthesis. I will describe how the lifetime of the hypermassive NS created during a NS-NS merger impacts the light curves and color of kilonovae. A small fraction of short gamma-ray bursts are accompanied by long-lived X-ray emission, which may suggest that some mergers result in the formation of long-lived - or even indefinitely stable - NS remnants. If this association is confirmed, this would place stringent constraints on the equation of state of nuclear density matter.