Physical and structural phenomena originating from polar discontinuities have generated enormous activity. In the last ten years, the oxide interface between polar LaAlO3 and non-polar SrTiO3, both band insulators, has attracted particular interest, as it hosts an electron liquid with remarkable properties: it superconducts, has a sizeable spin–orbit interaction and its properties are tunable by an electric field. The profile of the carrier density at the interface and the exact band structure are properties strongly linked and still objects of debate. Here we review the experimental findings on the origin and the extension of the electron liquid and discuss the theoretical models developed to describe the charge profile and the band structure. We also introduce a model to account for the effect of interface disorder which could modify the charge distribution.