Fast Radio Bursts (FRBs) are highly energetic, extremely short-lived bursts of radio flashes.
Despite extensive research, the exact cause of these outbursts remains a mystery. One of the
most accredited models suggests that they originate from highly magnetized and rapidly spinning
neutron stars known as magnetars. The high luminosity, short duration, and high dispersion
measure of these events suggest they result from extreme, high-energy astrophysical processes
of extragalactic origin. The number of detected FRBs, including repeating ones, has grown
rapidly in recent years. Except for FRB20200428, that is associated to the galactic magnetar
SGR1925+2154, no multi-wavelength counterparts to any FRB has been detected yet. The High
Energy Stereoscopic System (H.E.S.S.) telescope has developed a program to uncover the nature
of these mysterious events by searching for their gamma-ray counterparts. This contribution
provides an overview of the searches for FRB sources conducted by H.E.S.S., including follow-up
observations and simultaneous multi-wavelength campaigns with radio and X-ray observatories