Superconductivity in non-centrosymmetric materials can display various intriguing properties. Using the example of the CePt3Si a phenomenological description of this non-centrosymmetric superconductor is given, in an attempt to identify the symmetry of the Cooper pairing state. A short overview on other recently discovered non-centrosymmetric superconductors mainly, in strongly correlated electron systems, is given. (c) 2006 Elsevier B.V. All rights reserved.