This short review covers the emerging research field of interface superconductivity in complex oxide heterostructures. The first part of the paper is devoted to the prediction and observation of an interfacial superconducting state in metallic/insulating copper oxide bilayers. In the second part of the manuscript, the discovery and the modulation of superconductivity at the interface between two insulating oxides, LaAlO3 and SrTiO3, is described. These examples serve as an illustration of the potential that interfaces hold for revealing novel electronic behavior in complex oxide heterostructures, opening possibly a path to enhance the critical temperature or to discover new superconductors.