This Heraeus Seminar explores the joint role that particle physics and gravitational waves can play in telling us about the physics of the early Universe and the deep structure of matter. Physics topics include phase transitions in the early Universe, black holes (also in connection with dark matter candidates), dark energy, CMB polarisation as a probe of inflation, what the Higgs boson might be telling us as a clue to deeper physics and tiny neutrino masses and possible axion-like particles as probes of new physics at very high scales. The high luminosity upgrade of the LHC, the LISA