Positron emission tomography (PET) and magnetic resonance imaging (MRI) have both been used for decades in cardiovascular imaging. Since 2010, hybrid PET/MRI using sequential and integrated scanner platforms has been available, with hybrid cardiac PET/MR imaging protocols increasingly incorporated into clinical workflows. Given the range of complementary information provided by each method, the use of hybrid PET/MRI may be justified and beneficial in particular clinical settings for the evaluation of different disease entities. In the present joint position statement, we critically review the role and value of integrated PET/MRI in cardiovascular imaging, provide a technical overview of cardiac PET/MRI and practical advice related to the cardiac PET/MRI workflow, identify cardiovascular applications that can potentially benefit from hybrid PET/MRI, and describe the needs for future development and research. In order to encourage its wide dissemination, this article is freely accessible on the European Radiology and European Journal of Hybrid Imaging web sites.Key Points center dot Studies and case-reports indicate that PET/MRI is a feasible and robust technology.center dot Promising fields of application include a variety of cardiac conditions.center dot Larger studies are required to demonstrate its incremental and cost-effective value.center dot The translation of novel radiopharmaceuticals and MR-sequences will provide exciting new opportunities.