Causal graphical models, especially those involving hidden variables, have emerged as an important tool in applied research and as mathematically intriguing objects in their own right. In keeping with the theme of this programme, I will blend theory and practice in my treatment of these models. The first part of the tutorial covers the foundations of causal graphs—how they are defined, why they are useful, and classical identification results, including the g-formula, front-door formula, and an introduction to discrete parameterizations of these models. The tutorial also emphasizes results on non-identification, characterizing settings in which unbiased inference is impossible without additional assumptions. The second part provides a brief introduction to key ideas in model selection for adjudicating between competing causal models when there is model uncertainty. The overarching goal of the tutorial is to equip attendees with a fairly general framework and knowledge that allow them to engage more confidently with both theoretical and applied problems in causal inference.