A review is given of the results obtained by the method of tunnel spectroscopy in high-pressure studies of superconductivity, lattice properties, size quantization effects, and Andreev reflection. Experimental data on changes in the superconducting energy gap, its anisotropy, phonon spectra, and spectral electron-phonon interaction function are reported and analyzed. The limits of validity of approximate formulas for the critical temperature of a superconductor are discussed. Investigations are reported of the behavior of the electron phonon interaction and of vibrational spectra of the lattices of binary systems near the phase equilibrium boundaries. Studies of the influence of pressure on the quantum size effect in thin metal films and of interference effects in superconductor-normal metal layer structures are used to find the shift of the high-energy characteristics of the band structure and an increase in the Fermi velocity is reported. Potential applications of the method of electron tunneling in the physics of high pressures are discussed.