Oxide interfaces manifest many fascinating phenomena with synergetic correlations among multiple degrees of freedom, including the interplay of broken symmetry, lattice mismatch, charge transfer, spatial confinement, etc. In particular, the interface superconductivity in oxide heterostructures has attracted extensive attention due to the rich underline physics. Interfaces not only provide alternative research platforms with respect to the bulk material counterpart for exploration of new superconductors and investigating superconducting mechanisms, but also create new opportunities for promoting superconductors to future electronic devices. In recent years, thanks to the rapid development of heteroepitaxial techniques and accurate characterization methods, researchers have found quasi-two-dimensional interface superconductivity in various oxide heterostructures and revealed numerous novel quantum phenomena associated with interface superconductivity, which not only promote the development of condensed matter physics, but also lay important foundations for the practical application of interface superconductivity. In this brief review, we mainly focus on the discussion of the quasi-two-dimensional superconductivity at oxide interfaces. Taking the typical quasi-two-dimensional superconductivity at the LaAlO<sub>3</sub>/SrTiO<sub>3</sub> interface and copper oxides such as La<sub>2</sub>CuO<sub>4</sub>/La<sub>1.56</sub>Sr<sub>0.44</sub>CuO<sub>4</sub> as examples, we summarize and examine some novel physical phenomena with interface superconductivity in complex oxide heterostructures. Then we address the related problems that still exist in the research field at present, and finally we look forward to the future possible development of the interface superconductivity.