We present a representation of events and action based on interval temporal logic that is significantly more expressive and more natural than most previous AI approaches. The representation is motivated by work in natural language semantics and discourse, temporal logic, and AI planning and plan recognition. The formal basis of the representation is presented in detail, from the axiomatization of time periods to the relationship between actions and events and their effects. The power of the representation is illustrated by applying it to the axiomatization and solution of several standard problems from the AI literature on action and change. An approach to the frame problem based on explanation closure is shown to be both powerful and natural when combined with our representational framework. We also discuss features of the logic that are beyond the scope of many traditional representations, and describe our approach to difficult problems such as external event! and simultaneous actions.