  The recent milestones in multi-messenger astronomy have opened new ways to
study the Unverse. The unprecedented gravitational wave (GW) follow-up
campaigns established the power that the combination of different messengers
has to identify and study the nature and evolution of astrophysical phenomena.
Here we focus on the search for high-energy gamma ray emission as
electromagnetic counterpart of compact binary coalescences with the H.E.S.S.
Imaging Air Cherenkov Telescopes (IACTs). In this contribution, the optimized
strategies developed specifically for the prompt follow-up of gravitational
wave events with H.E.S.S are presented. As illustration, the successful
observation campaigns up to this time will be described, including the ones
during Observation Run O2 on the binary black hole (BH-BH) merger GW170814 and
the binary neutron star (NS-NS) merger GW170817, and an update on recent events
occurring during O3. Results of these searches are presented and the
constraints that prompt observations can put on very-high-energy, non-thermal
emission, are briefly discussed. Finally, an outlook on further improvements
for the gravitational waves follow-up program with H.E.S.S. will be provided.
