It is shown that the interplay between relativity and coherence, found in superconductors with heavy elements, leads to a number of interesting and previously unknown effects. In particular, several types of spinorbit coupling are shown to exist only in superconductors. Explicit expressions describing these effects are derived using a covariant formulation of the theory of superconductivity. It is demonstrated that relativistic effects can become relevant, e.g., in high-temperature and heavy-fermion superconductors, superconducting heterostructures, and rotating superconductors.