The theory of causality is based upon structural causal models which combine features of the structural equation models, the potential-outcome framework of Neyman and Rubin, and the causal graphical models developed for probabilistic reasoning and causal inference. In this framework, causal relationships are encoded in a causal graphical model that incorporates a finite set of nodes and edges representing the involved variables and causal relationships, respectively.
When the true causal structure is given, the so-called do-calculus allows for an identification of the causal effects in the observed system. Moreover, the relationships in the causal graph build the basis of estimation procedures to derive the functional relationships that allows to predict the result of an intervention to the system.