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This paper presents IntegriDB, a system allowing a data owner to outsource storage of a database to an untrusted server, and then enable anyone to perform verifiable SQL queries over that database. Our system handles a rich subset of SQL queries, including multidimensional range queries, JOIN, SUM, MAX/MIN, COUNT, and AVG, as well as (limited) nestings of such queries. Even for tables with 10⁵ entries, IntegriDB has small proofs (a few KB) that depend only logarithmically on the size of the database, low verification time (tens of milliseconds), and feasible server computation (under a minute). Efficient updates are also supported. We prove security of IntegriDB based on known cryptographic assumptions, and demonstrate its practicality and expressiveness via performance measurements and verifiable processing of SQL queries from the TPC-H and TPC-C benchmarks.