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Many modern histopathology laboratories are in the process of digitizing their workflows. Digitization of tissue images has made it feasible to research the augmentation or automation of clinical reporting and diagnosis. The application of modern computer vision techniques, based on deep learning, promises systems that can identify pathologies in slide images with a high degree of accuracy. Generative modeling is an approach to machine learning and deep learning that can be used to transform and generate data. It can be applied to a broad range of tasks within digital pathology, including the removal of color and intensity artifacts, the adaption of images in one domain into those of another, and the generation of synthetic digital tissue samples. This review provides an introduction to the topic, considers these applications, and discusses future directions for generative models within histopathology.