  The first direct measurement of gravitational waves by the LIGO and Virgo
collaborations has opened up new avenues to explore our Universe. This white
paper outlines the challenges and gains expected in gravitational wave searches
at frequencies above the LIGO/Virgo band, with a particular focus on Ultra
High-Frequency Gravitational Waves (UHF-GWs), covering the MHz to GHz range.
The absence of known astrophysical sources in this frequency range provides a
unique opportunity to discover physics beyond the Standard Model operating both
in the early and late Universe, and we highlight some of the most promising
gravitational sources. We review several detector concepts which have been
proposed to take up this challenge, and compare their expected sensitivity with
the signal strength predicted in various models. This report is the summary of
the workshop "Challenges and opportunities of high-frequency gravitational wave
detection" held at ICTP Trieste, Italy in October 2019, that set up the stage
for the recently launched Ultra-High-Frequency Gravitational Wave (UHF-GW)
initiative.
