Positron emission tomography (PET) imaging has made it possible to detect the in vivo concentration of positron-emitting compounds accurately and non-invasively. In order to relate the radioactivity concentration measured using PET to the underlying physiological or biochemical processes, the application of mathematical models to describe tracer kinetics within a particular region of interest is necessary. Image analysis can be performed both by visual interpretation and quantitative assessment and, depending on the ultimate purposes of the analysis, several alternatives are available. In clinical practice, PET quantification is routinely performed using the standard uptake value (SUV), a semiquantitative index in use since the 1980s. Its computation is very simple since it requires only the PET measure at a prefixed sample time and the injected dose normalised to some anthropometric characteristic of the subject (generally body weight or body surface area). An alternative to the SUV is the tissue-to-plasma ratio (ratio). As its name indicates, this index is computed as the ratio between the tracer activity measured in the tissue and in the plasma pool within a prefixed time window. Moving from static to more informative dynamic PET acquisition, three model classes represent the most frequently used approaches: compartmental models, the spectral analysis modelling approach, and graphical methods. These approaches differ in terms of application assumptions (e.g. reversibility of tracer uptake, model structure, etc.) and computational complexity. They also produce different information about the system under study: from a macro-description of tracer uptake to a full quantitative characterisation of the physiological processes in which the tracer is involved. The application of these approaches to clinical routine is restricted by the need for invasive blood sampling. In order to avoid arterial cannulation and blood sample management, different alternative approaches have been developed for quantification of PET kinetics, including reference tissue methods. Although these approaches are appealing, the results obtained with several tracers are questionable. This review provides a complete overview of the semi-quantitative and quantitative methods used in PET analysis. The pros and cons of each method are evaluated and discussed.