Superbursts were discovered at the beginning of this millennium. Just like type-I X-ray bursts, they are thought to be due to thermonuclear shell flashes on neutron stars, only igniting much deeper. With respect to type-I bursts, they last 10$^3$ times longer, are 10$^3$ as rare, ignite 10$^3$ times deeper (in column depth) and are thought to be fueled by carbon instead of hydrogen and helium. Observationally, they are sometimes hard to distinguish from intermediate duration bursts which are due to pure helium flashes on cold neutron stars. So far, 26 superbursts have been detected from 15 neutron stars in low-mass X-ray binaries that also exhibit type-I bursts. They are very difficult to catch and only 2 have been measured with highly sensitive instrumentation. Superbursts are sensitive probes of the neutron star crust and the accretion disk. The superburst phenomenon is not fully understood. Questions remain about the nature of the fuel, the collection of that fuel and the ignition conditions. The current state of affairs is reviewed and possible resolutions that lay ahead in the future discussed.