Creating semantic matches between disparate data sources is fundamental to numerous data sharing efforts. Manually creating matches is extremely tedious and error-prone. Hence many recent works have focused on automating the matching process. To date, however, virtually all of these works deal only with one-to-one (1-1) matches, such as address = location. They do not consider the important class of more complex matches, such as address = concat (city, state) and room-pric = room-rate* (1 + tax-rate).We describe the iMAP system which semi-automatically discovers both 1-1 and complex matches. iMAP reformulates schema matching as a search in an often very large or infinite match space. To search effectively, it employs a set of searchers, each discovering specific types of complex matches. To further improve matching accuracy, iMAP exploits a variety of domain knowledge, including past complex matches, domain integrity constraints, and overlap data. Finally, iMAP introduces a novel feature that generates explanation of predicted matches, to provide insights into the matching process and suggest actions to converge on correct matches quickly. We apply iMAP to several real-world domains to match relational tables, and show that it discovers both 1-1 and complex matches with high accuracy.