Information integration is becoming a critical problem for both businesses and individuals. The data, especially the one that comes from the Web, is naturally incomplete, that is, some data values may be unknown or lost because of communication problems, hidden due to privacy considerations. At the same time research in (virtual) integration in the community focusses on null-free sources and addresses limited forms of incompleteness only. In our work we aim to extend current results on virtual integration by considering various forms of incompleteness at the level of sources, integrated databases and queries. We term this Incomplete Information Integration, or III. More specifically, we aim to extend current query answering techniques for local-, and global-as-view integration to integration of tables with SQL nulls, and various forms of c-tables. We also aim to consider incomplete answers as a natural extension of the classical approach, that is, certain answers. Our main research issues are: (1) semantics of III; (2) semantics of query answering in III (3) complexity of query answering, and (4) algorithms (possibly approximate) to compute the answers.