Lexical semantics and logical semantics have traditionally different tools to address distinct aspects of semantic composition. Lexical semantics focuses on the meanings of individual words, while logical semantics studies the compositional properties of propositional interpretations (e.g., attitudes and judgments). As events and event structure have entered the field as representational devices, these two approaches have moved closer together: lexical semanticists must look outward from the verb to the sentence in order to characterize the effects of a verb's event structure; and logical semanticists must look inward from the sentence to the verb to represent semantic facts that depend on event-related properties of particular verbs. Concurrently, syntacticians have discovered phenomena in which the semantics of events can be seen to interact with syntactic structures, and have had to turn to semanticists for representations of the properties associated with events. The mapping between syntax and event structure has emerged as an important area of research. The discoveries that are being made in these different areas about the role of events in natural language must, in the last analysis, be connected. This volume is intended to take some steps towards an integrated theory of events in the grammar of natural language. Both the diversity and the convergence of these various syntactic and semantic approaches is reflected in this volume of papers. This introduction will attempt to put the papers in a common context, and orient them towards a common vision.