Non-rotating neutron stars are expected to cool down to unobservably low temperatures within less than 10 Myr. However, all known neutron stars are rotating at a slowly decreasing rate, which has been proposed to re-heat old neutron stars by two proceses: 1) Vortex creep, the dissipative motion of quantized vortices through the neutron superfluid expected to exist in the neutron star crust (Alpar et al. 1984), and 2) Rotochemical heating, the energy released by non-equilibrium beta decays due to the slow contraction of the neutron star as its centrifugal force decreases (Reisenegger 1995, 1997; Fernandez & Reisenegger 2005; Petrovich & Reiseneg-ger 2010, 2011; González-Jiménez, Petrovich, & Reisenegger 2015). Both processes are quite model-dependent, but can naturally keep millisecond pulsars at a surface temperature ~10^5K, at which their thermal radiation should be observed in the far ultraviolet, as appears to be the case in HST observations of the closest millisecond pulsar, PSR J0437-4715 (Kargaltsev et al. 2004; Durant et al. 2012). Far-ultraviolet observations of other old pulsars, which are currently being attempted, should allow to distinguish between the two plausible heating processes and constrain the internal structure of neutron stars and the physics of very dense matter (Gonzalez & Reisenegger 2010).