Exogenous heterogeneity, for example in the form of instrumental variables, can help us learn a system's underlying causal structure and predict the outcome of unseen intervention experiments. In this talk, we discuss this idea in a setting in which the causal effect from covariates on the response is sparse and in a setting, where the variables follow a time dependence structure. If time allows, we also briefly discuss what can be done when identifiability conditions are not satisfied.