The first direct observations of gravitational waves (GWs) by ground-based interferometers have ushered in the era of GW astronomy. While the central focus of such experiments has been on the Hz − kHz frequency range, an exploration across a much wider spectrum is warranted. The Universe is expected to be populated by GWs over many decades in frequency, analogous to electromagnetic radiation. In this talk I will first discuss several high-frequency GW sources, in particular GWs from the thermal plasma and several late universe sources. In the main part of this talk I will then consider electromagnetic signals of high-frequency GWs in cavities. I will explain why a gauge invariant description of the signal is important and show that existing axion experiments can already search for high-frequency GWs.

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