Accurate quantification in PET and SPECT requires correction for a number of physical factors, such as photon attenuation, Compton scattering and random coincidences (in PET). Another factor affecting quantification is the limited spatial resolution. While considerable effort has gone into development of routine correction techniques for the former factors, less attention has been paid to the latter. Spatial resolution-related effects, referred to as 'partial volume effects' (PVEs), depend not only on the characteristics of the imaging system but also on the object and activity distribution. Spatial and/or temporal variations in PVE can often be confounding factors. Partial volume correction (PVC) could in theory be achieved by some kind of inverse filtering technique, reversing the effect of the system PSF. However, these methods are limited, and usually lead to noise-amplification or image artefacts. Some form of regularization is therefore needed, and this can be achieved using information from co-registered anatomical images, such as CT or MRI. The purpose of this paper is to enhance understanding of PVEs and to review possible approaches for PVC. We also present a review of clinical applications of PVC within the fields of neurology, cardiology and oncology, including specific examples.