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The need for timely processing large amounts of information, flowing from the peripheral to the center of a system, is common to different application domains, and it has justified the development of several languages to describe how such information has to be processed. In this paper, we analyze such languages showing how most approaches lack the expressiveness required for the applications we target, or do not provide the precise semantics required to clearly state how the system should behave. Moving from these premises, we present TESLA, a complex event specification language. Each TESLA rule considers incoming data items as notifications of events and defines how certain patterns of events cause the occurrence of others, said to be "complex". TESLA has a simple syntax and a formal semantics, given in terms of a first order, metric temporal logic. It provides high expressiveness and flexibility in a rigorous framework, by offering content and temporal filters, negations, timers, aggregates, and fully customizable policies for event selection and consumption. The paper ends by showing how TESLA rules can be interpreted by a processing system, introducing an efficient event detection algorithm based on automata.