Positron emission tomography (PET) is actively used in a diverse range of applications in oncology, cardiology, and neurology. The use of PET in the clinical setting focuses on static (single time frame) imaging at a specific time-point post radiotracer injection and is typically considered as semi-quantitative; e.g. standardized uptake value (SUV) measures. In contrast, dynamic PET imaging requires increased acquisition times but has the advantage that it measures the full spatiotemporal distribution of a radiotracer and, in combination with tracer kinetic modeling, enables the generation of multiparametric images that more directly quantify underlying biological parameters of interest, such as blood flow, glucose metabolism, and receptor binding. Parametric images have the potential for improved detection and for more accurate and earlier therapeutic response assessment. Parametric imaging with dynamic PET has witnessed extensive research in the past four decades. In this paper, we provide an overview of past and present activities and discuss emerging opportunities in the field of parametric imaging for the future.