  This article is a pedagogical review of theoretical studies of
noncentrosymmetric superconductors with particular emphasis on the role played
by electron correlation, which is important for heavy fermion systems. We
survey unique properties of parity-violated superconductivity such as the
admixture of spin singlet and triplet states, unusual paramagnetism, large
Pauli limiting fields, magnetoelectric effects, the helical vortex phase, and
the anomalous Hall effect. It is pointed out that these remarkable features are
strengthened by a strong electron correlation effect, and thus are prominent in
heavy fermion superconductors without inversion symmetry. We also discuss
possible pairing states realized in the heavy fermion system CePt$_3$Si.
