With this document, we provide a standard for PET/(diagnostic) CT imaging procedures in cardiovascular diseases that are inflammatory, infective, infiltrative, or associated with dysfunctional innervation (4Is). This standard should be applied in clinical practice and integrated in clinical (multicenter) trials for optimal procedural standardization. A major focus is put on procedures using [¹⁸F]FDG, but 4Is PET radiopharmaceuticals beyond [¹⁸F]FDG are also described in this document. Whilst these novel tracers are currently mainly applied in early clinical trials, some multicenter trials are underway and we foresee in the near future their use in clinical care and inclusion in the clinical guidelines. Finally, PET/MR applications in 4Is cardiovascular diseases are also briefly described. Diagnosis and management of 4Is-related cardiovascular diseases are generally complex and often require a multidisciplinary approach by a team of experts. The new standards described herein should be applied when using PET/CT and PET/MR, within a multimodality imaging framework both in clinical practice and in clinical trials for 4Is cardiovascular indications.