This report of an ESC Study Group reviews current knowledge on myocardial hibernation and relevant imaging techniques, and provides an algorithm for investigation and management when a patient presents with ischaemic left ventricular dysfunction. It covers the definitions of myocardial viability, stunning and hibernation, it reviews the morphological findings in hibernation and it describes relevant clinical settings. The imaging and other techniques that are reviewed are electrocardiography, positron-emitting and single photon-emitting scintigraphic imaging, echocardiography, radionuclide angiocardiography, magnetic resonance imaging, X-ray transmission tomography, invasive X-ray angiocardiography and electromechanical mapping. The evidence for the techniques to predict improvement of regional and global function after revascularisation is summarised and patient symptoms and clinical outcome are also considered. Each technique is classified in its ability to assess myocardial viability, function and perfusion and also for their roles in the assessment of the patient with ischaemic left ventricular dysfunction who is asymptomatic or who has angina or heart failure. A simplified clinical algorithm describes the initial assessment of left ventricular function, then viability and then perfusion reserve allowing regions of myocardium to be characterised as transmural scar, intramural scar, hibernation or ischaemia.