Integrating multiple heterogeneous data sources into applications is a time-consuming, costly and error-prone engineering task. Relatively mature technologies exist that make integration tractable from an engineering perspective. These technologies, however, have many limitations, and hence present opportunities for breakthrough research. This paper briefly describes some of these limitations, and enumerates a subset of the general open research problems. It then describes the Data Concierge research project and prototype that is attempting to provide solutions to some of these problems.