In nuclear medicine, clinical assessment and diagnosis are generally based on qualitative assessment of the distribution pattern of radiotracers used. In addition, emission tomography (SPECT and PET) imaging methods offer the possibility of quantitative assessment of tracer concentration in vivo to quantify relevant parameters in clinical and research settings, provided accurate correction for the physical degrading factors (e.g. attenuation, scatter, partial volume effects) hampering their quantitative accuracy are applied. This review addresses the problem of Compton scattering as the dominant photon interaction phenomenon in emission tomography and discusses its impact on both the quality of reconstructed clinical images and the accuracy of quantitative analysis. After a general introduction, there is a section in which scatter modelling in uniform and non-uniform media is described in detail. This is followed by an overview of scatter compensation techniques and evaluation strategies used for the assessment of these correction methods. In the process, emphasis is placed on the clinical impact of image degradation due to Compton scattering. This, in turn, stresses the need for implementation of more accurate algorithms in software supplied by scanner manufacturers, although the choice of a general-purpose algorithm or algorithms may be difficult.