Dynamic contrast-enhanced computed tomography (DCE-CT) and magnetic resonance imaging (DCE-MRI) are functional imaging techniques. They aim to characterise the microcirculation by applying the principles of tracer-kinetic analysis to concentration-time curves measured in individual image pixels. In this paper, we review the basic principles of DCE-MRI and DCE-CT, with a specific emphasis on the use of tracer-kinetic modeling. The aim is to provide an introduction to the field for a broader audience of pharmacokinetic modelers. In a first part, we first review the key aspects of data acquisition in DCE-CT and DCE-MRI, including a review of basic measurement strategies, a discussion on the relation between signal and concentration, and the problem of measuring reference data in arterial blood. In a second part, we define the four main parameters that can be measured with these techniques and review the most common tracer-kinetic models that are used in this field. We first discuss the models for the capillary bed and then define the most general four-parameter models used today: the two-compartment exchange model, the tissue-homogeneity model, the "adiabatic approximation to the tissue-homogeneity model" and the distributed-parameter model. In simpler tissue types or when the data quality is inadequate to resolve all the features of the more complex models, it is often necessary to resort to simpler models, which are special cases of the general models and hence have less parameters. We discuss the most common of these special cases, i.e. the uptake models, the extended Tofts model, and the one-compartment model. Models for two specific tissue types, liver and kidney, are discussed separately. We conclude with a review of practical aspects of DCE-CT and DCE-MRI data analysis, including the problem of identifying a suitable model for any given data set, and a brief discussion of the application of tracer-kinetic modeling in the context of drug development. Here, an important application of DCE techniques is the derivation of quantitative imaging biomarkers for the assessment of effects of targeted therapeutics on tumors.