Of the three main types of binaries detectable through ground-based gravitational wave observations, black hole-neutron star (BHNS) mergers remain the most elusive. While candidates BHNS exist in the triggers released during the third observing run of the Advanced LIGO/Virgo collaboration, no detection has been confirmed so far. As for binary neutron star systems, BHNS binaries allow us to explore a wide range of physical processes, including the neutron star equation of state, nucleosynthesis, stellar evolution, high-energy astrophysics, and the expansion of the Universe. Here, we review some of the main features of BHNS systems: the distinction between disrupting and non-disrupting binaries, the types of outflows that BHNS mergers can produce, and the information that can be extracted from the observation of their gravitational wave and electromagnetic signals. We also emphasize that for the most likely binary parameters, BHNS mergers seem less likely to power electromagnetic signals than binary neutron star systems. Finally, we discuss some of the issues that still limit our ability to model and interpret electromagnetic signals from BHNS binaries.