Studies evaluating the diagnostic performance of coronary computed tomography angiography (CTA) are consistent in demonstrating a high negative predictive accuracy, but only a modest positive predictive accuracy for the detection of significant coronary artery disease. Consequentially, there has been a considerable effort made to enhance the diagnostic capability of coronary CTA by developing scanner technology and also post-processing algorithms for coronary stenosis evaluation. Of these new developments, the proposition of being able to measure non-invasive fractional flow reserve by coronary computed tomography angiography (FFRct) has generated much recent interest. Initial reports indicate that the application FFRct not only correlates well with invasive fractional flow reserve but also has the potential to enhance substantially the positive predictive accuracy and overall accuracy of coronary CTA. Although it is theoretically possible to measure FFRct using complex computational fluid dynamics adapted from the aeronautical industry, this approach is likely to face a number of challenges prior to it being accepted into the mainstream as an adjunct to coronary CTA. The aim of the current review is to provide an overview of: 1) the fundamental engineering principles behind computational fluid dynamic modelling of coronary arterial blood flow; 2) the difficulties faced from an engineering perspective in developing a truly representative model; and 3) the challenges this technology is likely to face as it attempts to enter the clinical domain.