Detection of scattered gamma quanta degrades image contrast and quantitative accuracy of single-photon emission computed tomography (SPECT) imaging. This paper reviews methods to characterize and model scatter in SPECT and correct for its image degrading effects, both for clinical and small animal SPECT. Traditionally scatter correction methods were limited in accuracy, noise properties and/or generality and were not very widely applied. For small animal SPECT, these approximate methods of correction are often sufficient since the fraction of detected scattered photons is small. This contrasts with patient imaging where better accuracy can lead to significant improvement of image quality. As a result, over the last two decades, several new and improved scatter correction methods have been developed, although often at the cost of increased complexity and computation time. In concert with (i) the increasing number of energy windows on modern SPECT systems and (ii) excellent attenuation maps provided in SPECT/CT, some of these methods give new opportunities to remove degrading effects of scatter in both standard and complex situations and therefore are a gateway to highly quantitative single- and multi-tracer molecular imaging with improved noise properties. Widespread implementation of such scatter correction methods, however, still requires significant effort.