This dissertation presents the Temporal Event Query Language (TEQL), a new language for querying event streams. Event Stream Processing enables online querying of streams of events to extract relevant data in a timely manner. TEQL enables querying of interval-based event streams using temporal database operators. Temporal databases and temporal query languages have been a subject of research for more than 30 years and are a natural fit for expressing queries that involve a temporal dimension. However, operators developed in this context cannot be directly applied to event streams. The research extends a preexisting relational framework for event stream processing to support temporal queries. The language features and formal semantic extensions to extend the relational framework are identified. The extended framework supports continuous, step-wise evaluation of temporal queries. The incremental evaluation of TEQL operators is formalized to avoid re-computation of previous results. The research includes the development of a prototype that supports the integrated event and temporal query processing framework, with support for incremental evaluation and materialization of intermediate results. TEQL enables reporting temporal data in the output, direct specification of conditions over timestamps, and specification of temporal relational operators. Through the integration of temporal database operators with event languages, a new class of temporal queries is made possible for querying event streams. New features include semantic aggregation, extraction of temporal patterns using set operators, and a more accurate specification of event co-occurrence.