H.E.S.S. observations following multi-messenger alerts in real-time

The H.E.S.S. Imaging Air Cherenkov Telescope system is, due to its fast reaction time and its comparably low energy threshold, very well suited to perform follow-up observations of detections at other wavelengths or other messengers like high-energy neutrinos and gravitational waves. These advantages are utilized optimally via a fully automatized system reacting to alerts from various partner observatories covering various wavelengths and astrophysical messengers. In this contribution we'll provide an overview and present recent results from H.E.S.S. programs to follow up on multi-wavelength and multi-messenger alerts. To illustrate the capabilities of the system we present several real-time ToO observations searching for high-energy gamma-ray emission in coincidence with high-energy neutrinos detected by the IceCube and ANTARES neutrino telescopes and outline our program to search for gravitational wave counterparts.