A review of heavy-fermion compounds investigated in their normal and superconducting states by point-contact spectroscopy is presented. The Joule heating appears to have a considerable influence on the conductivity in metallic point contacts in both the normal and superconducting states. Nonetheless, some spectroscopic information can be obtained from the point-contact measurements, and Josephson effects are observed for certain heavy-fermion superconductors. We review in detail very recent development in this field, including experiments using mechanically controllable break junctions covering the regime from metallic conductivity to truly vacuum tunnelling.