Over the past 20 years morphologic imaging of various tumors and tissues experienced substantial progress by the introduction of ultrasonography, CT scanning and MRI. None of these techniques provide information on functional aspects. Positron-emission tomography (PET) now allows to measure local perfusion, oxygen extraction and glucose utilisation in different tissues. These 3 parameters do not necessarily develop in parallel and can potentially be differentiated by PET. Thus, they become detectable in brain tumors as well as in vascular and degenerative dementias and, therefore, directly permit therapeutic measures. In brain tumors PET is clinically useful today for grading and therapy control by means of FDG (18fluoro-deoxyglucose) and amino-acids. Postoperatively it allows differentiation of tumor recurrence from scar-tissue, fibrosis and necrosis. In dementias of different etiologies possible fields of application for the PET lie in differentiation between dementias of vascular origin and Alzheimer's disease as well as in control of therapy (FDG).