We present WSQ/DSQ (pronounced "wisk-disk"), a new approach for combining the query facilities of traditional databases with existing search engines on the Web. WSQ, for Web-Supported (Database) Queries, leverages results from Web searches to enhance SQL queries over a relational database. DSQ, for Database-Supported (Web) Queries, uses information stored in the database to enhance and explain Web searches. This paper focuses primarily on WSQ, describing a simple, low-overhead way to support WSQ in a relational DBMS, and demonstrating the utility of WSQ with a number of interesting queries and results. The queries supported by WSQ are enabled by two virtual tables, whose tuples represent Web search results generated dynamically during query execution. WSQ query execution may involve many high-latency calls to one or more search engines, during which the query processor is idle. We present a lightweight technique called asynchronous iteration that can be integrated easily into a standard sequential query processor to enable concurrency between query processing and multiple Web search requests. Asynchronous iteration has broader applications than WSQ alone, and it opens up many interesting query optimization issues. We have developed a prototype implementation of WSQ by extending a DBMS with virtual tables and asynchronous iteration; performance results are reported.