Artificially layered superlattices of oxide materials have been intensely investigated for some time, but continue to reveal new potential as a route to advanced functional materials. As well as considering electrostatics and strain, a more complete picture of the interfaces in these systems also needs to incorporate the possibility of additional structural distortions, electronic redistributions, and complex polarization domain structures. Here we focus on superlattices composed of two perovskite oxide materials, where one is a ferroelectric, and discuss the important interactions between the component materials that determine the behavior of the new artificial material. We discuss interfaces both with and without electronic screening. The first class of interface contains technologically relevant ultrathin ferroelectric capacitors and the more recently studied ferroelectric-metal superlattices. In these systems, the influence of the ferroelectric polarization decreases rapidly with distance from the interface. By contrast, in systems where the materials adjacent to the ferroelectric layers are dielectrics, the polarization of the ferroelectric layer influences the properties of the adjacent layers over a much longer distance, setting the stage for fascinating competition between the properties of the combined materials.