In recent years, gravitational-wave observations of neutron star-black hole (NSBH) mergers have brought these systems into the spotlight. The intrinsic mass asymmetry of NSBH binaries enhances subdominant multipoles in the gravitational-wave signal, helping to break degeneracies among the binary mass ratio, component spins, orbital inclination, and luminosity distance. This makes NSBH mergers particularly powerful laboratories for precision gravitational-wave inference: they can probe compact binary formation and evolution, enable measurements of even small neutron star spins, and serve as standard sirens for cosmology. Moreover, if the neutron star is tidally disrupted by the black hole, the merger can produce an electromagnetic counterpart, opening an important avenue for multi-messenger observations. In this talk, I will review the emerging observational landscape of NSBH mergers and discuss their scientific potential with current, upgraded, and next-generation gravitational-wave observatories. I will highlight prospects for precision measurements of binary parameters, electromagnetic follow-up, and standard siren cosmology, including the possibility of probing the cosmic expansion history at sub-percent precision with facilities such as Cosmic Explorer and the Einstein Telescope.