Two key symmetries underlie the formation of superconductivity: parity and time reversal. Breaking time reversal symmetry through the application of magnetic fields is known to be harmful to superconductors. The role of breaking parity symmetry is less well understood. However, this has become an important issue with the recent discovery of superconductivity at SrTiO 3 /LaAlO 3 interfaces and with the large number of superconductors with structures that lack parity symmetry. In this talk, after a discussion on the role of symmetry on superconductivity, I will contrast the physics with and without parity symmetry. This will include: the spin susceptibility in the superconducting state; the appearance of nodes in the superconducting gap driven by broken parity symmetry; and new physics that appears due to the application of magnetic fields.