According to the classical nineteenth century worldview, physical systems followed precisely defined trajectories that evolved according to deterministic laws. Physical theory was causally closed, having no place for interventions into its unfolding. Early in the twentieth century, this classical picture was overturned by a new fundamental physical theory. Unlike its classical predecessor, quantum theory is stochastic and causally open. Quantum theory represents not only the passive evolution of closed physical systems, but also the effects of interventions. According to quantum theory, the behavior of a quantum system in response to interventions is intrinsically unpredictable and follows a stochastic law. Stochastic theories of the effects of interventions have become popular recently in artificial intelligence. In these theories, the behavior of an undisturbed system is represented as a graph in which nodes represent variables and directed arcs represent cause and effect relationships. A causal theory specifies both the behavior of the undisturbed system and how it responds to interventions. Interventions act as local surgery to cut the causal links into one or more manipulated variables, and to set the manipulated variables to values specified from outside the model. This paper describes quantum theory as a theory of the effects of interventions, relates it to currently popular theories of causality, and formalizes quantum evolution in terms of graphical probability models defined on density operators.