We introduce a novel event-driven continuous time Bayesian network (ECTBN) representation to model situations where a system’s state variables could be influenced by occurrences of events of various types. In this way, the model parameters and graphical structure capture not only potential “causal” dynamics of system evolution but also the influence of event occurrences that may be interventions. Our model is applicable in numerous domains, including health care, politics, and finance. We propose a greedy search procedure for structure learning based on the BIC score for a special class of ECTBNs; this is asymptotically consistent and also effective for limited data. We demonstrate the representation’s power by applying it to model paths out of poverty for clients of CityLink Center, a non-profit integrated social service provider in Cincinnati, USA. The ECTBN captures the effect of classes/counseling sessions on an individual’s life outcome areas such as education, transportation, employment and financial education.