  We review the status of quasi-degenerate doublets in nuclei, called
pseudospin doublets, which were discovered about thirty years ago and the
origins of which have remained a mystery, until recently. We show that
pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian
which occurs when the sum of the scalar and vector potentials is a constant.
Furthermore, we survey the evidence that pseudospin symmetry is approximately
conserved in nuclear spectra and eigenfunctions and in nucleon-nucleus
scattering for a Dirac Hamiltonian with realistic nuclear scalar and vector
potentials.

Nuclear Theory