We present the design of a structured search engine which returns a multi-column table in response to a query consisting of keywords describing each of its columns. We answer such queries by exploiting the millions of tables on the Web because these are much richer sources of structured knowledge than free-format text. However, a corpus of tables harvested from arbitrary HTML web pages presents huge challenges of diversity and redundancy not seen in centrally edited knowledge bases. We concentrate on one concrete task in this paper. Given a set of Web tables T1, . . ., Tn, and a query Q with q sets of keywords Q1, . . ., Qq, decide for each Ti if it is relevant to Q and if so, identify the mapping between the columns of Ti and query columns. We represent this task as a graphical model that jointly maps all tables by incorporating diverse sources of clues spanning matches in different parts of the table, corpus-wide co-occurrence statistics, and content overlap across table columns. We define a novel query segmentation model for matching keywords to table columns, and a robust mechanism of exploiting content overlap across table columns. We design efficient inference algorithms based on bipartite matching and constrained graph cuts to solve the joint labeling task. Experiments on a workload of 59 queries over a 25 million web table corpus shows significant boost in accuracy over baseline IR methods.