Interfaces between materials give rise to fascinating phenomena, and form the basis for much of modern technology. In the complex oxides, materials with very diverse properties can be brought together at atomically sharp interfaces. It is widely believed that such interfaces may provide an opportunity for the correlated degrees of freedom in these materials to "reconstruct" in novel ways, giving rise to new collective states. LaMnO3 and SrMnO3, both antiferromagnetic insulators, are end members of the La1-xSrxMnO3 phase diagram which includes a highly spin-polarized ferromagnetic metal and a variety of orbital-ordered antiferromagnets. We have synthesized superlattices of (LaMnO3)p/(SrMnO3)q using ozone-assisted molecular beam epitaxy (p,q are integers). In this talk, I will discuss the properties of these "digital manganites" for a range of p/q, including enhanced ordering temperatures compared to bulk samples, interfacial ferromagnetism, and the underlying interfacial proximity effects that may be responsible for their emergent properties.