This is a copy of the slides presented at the meeting but not formally written up for the volume.

Complex oxides show a broad spectrum of intrinsic functionalities, such as ferroelectricity, magnetism, superconductivity or multiferroic behavior, which can be utilized and combined in electronic devices by the growth and design of heterostructures. Physical properties may arise in such multilayers that are not found in either of their constituents. A spectacular example for such a phenomenon, a conducting and highly mobile electron gas, is formed at the interface between the two insulating, dielectric perovskites LaAlO3 and SrTiO3 [1] which can be easily tuned by transverse electric fields [2]. In our contribution we will present recent studies of the microstructure of the multilayer and we will correlate them with the transport properties of the electron gas. [1] A. Ohtomo, H. Y. Hwang, Nature 427, 423-426 (2004). [2] S. Thiel, G. Hammerl, A. Schmehl, C. W. Schneider, J. Mannhart, Science 313, 1942-1945 (2006).