CQL, a Continuous Query Language, is supported by the STREAM prototype Data Stream Management System at Stanford. CQL is an expressive SQL-based declarative language for registering continuous queries against streams and updatable relations. We begin by presenting act semantics that relies only on "black box" mappings among streams and relations. From these mappings we define a precise and general interpretation for continuous queries. n instantiation of our abstract semantics using SQL to map from relations to relations, window specifications derived from SQL-99 to map from streams to relations, and three new operators to map from relations to streams. Most of the CQL language is operational in the STREAM system. We present the structure of CQL's query execution plans as well as details of the most important components: operators, inter-operator queues, synopses, and sharing of components among multiple operators and queries. Examples throughout the paper are drawn fro...