The outcome of coronary revascularisation is not only defined by primary technical success, but also by improvement of symptoms and quality of life. Thus, despite the individual comorbidities, the outcome and thus the potential benefit of coronary revascularisation depends on many different factors, including morphology, distribution and severity of coronary lesions, myocardial viability, and ventricular function. Consequently, the detection of coronary stenosis is not sufficient for planning an optimised treatment, and more information is needed to personalise the treatment plan. It should be evaluated if the myocardial territory supported by the diseased artery is still vital and lesions at risk for plaque rupture (culprit lesions) should be the detector. These various approaches to obtaining energy-dependent measurements have different dose efficiency and different sensitivity to subject motion. The simplest method to process the multi-energy data reconstructs CT images from each spectrum and performs the multi-energy analysis on the reconstructed images. A somewhat preferred method performs energy-dependent processing on the raw projections prior to reconstruction. Hybrid methods are now available. Filtered backprojection (FBP) is currently the standard reconstruction algorithm in CT. FBP is fast and performs very well in many cases. FBP assigns the same certainty to all projections. In reality, the reliability of the projection data depends on the attenuation along the projection lines. As a result, FBP is suboptimal for noisy data. Performance in the presence of noise can be improved either by certainty based preprocessing of the projection data or by using iterative reconstruction algorithms based on a more realistic noise model. If the number of projection angles is limited, FBP suffers from artefacts. In contrast, iterative reconstruction is more robust against angular sampling issues. Nonetheless, if the number of projection angles is too low, there is not enough information for perfect reconstruction, and any algorithm will have problems finding the true solution. The problem can be alleviated by using prior knowledge about the object to be reconstructed. An example is the currently very popular total variation prior, which assumes that the reconstructed object should be piecewise uniform.