Molecular imaging can effectively diagnose and follow disease processes at the molecular and cellular level in a non-invasive manner. This is an extremely powerful method, enabling whole-body visualization, thus avoiding sampling error and dilution effects. Among the molecular imaging techniques, positron emission tomography (PET) is the most sensitive method and truly quantitative. PET can be combined with CT as PET/CT, a method that has become indispensable for diagnosing and treating patients with cancer. Recently PET/MRI was introduced, allowing for anatomical and simultaneous functional imaging with two modalities. Though PET has mainly been used within oncology and cardiovascular diseases, its potential to identify and follow the development of infection, inflammation and rejection processes is relatively poorly studied.