Over the last decade, steady progress has been made in the ability to assess coronary stenosis relevance by merging computerised analyses of angiograms with fluid dynamic modelling. The new field of functional coronary angiography (FCA) has attracted the attention of both clinical and interventional cardiologists as it anticipates a new era of facilitated physiological assessment of coronary artery disease, without the need for intracoronary instrumentation or vasodilator drug administration, and an increased adoption of ischaemia-driven revascularisation. This state-of-the-art review performs a deep dive into the foundations and rationale behind FCA indices derived from either invasive or computed angiograms. We discuss the currently available FCA systems, the evidence supporting their use, and the specific clinical scenarios in which FCA might facilitate patient management. Finally, the rapidly growing application of FCA to the diagnosis of coronary microvascular dysfunction is discussed. Overall, we aim to provide a state-of-the-art review not only to digest the achievements made so far in FCA, but also to enable the reader to follow the many publications and developments in this field that will likely take place in years to come.