Historical highlights of studies of current flow across metal-semiconductor contacts via electron tunneling are outlined. The physical origin of the space-charge potential at a rectifying metal contact on a degenerate semiconductor is illustrated with emphasis on the features of this potential which determine the dominant mechanism of current flow across the contact. Recent experiments on the tunneling characteristics of these junctions are described. Their interpretation in terms of phenomenological independent-electron models is discussed critically. The tunneling spectroscopy of collective excitations is described by use of the transfer-Hamiltonian model. The influence of features of the phonon spectra in the semiconductor on inelastic tunneling is illustrated for Ge. The effects of electronic interactions with collective excitations in the semiconductor electrode are discussed for phonons in Si and CdS, and for plasmons in GaAs. The references given herein supplement those presented in a recent comprehensive review.