Over the past several years, we have witnessed the impressive progress of cross-domain image generation based on deep learning approaches. It is attracting increasing attention because of its promising performance on a wide range of computer vision and image processing applications. In this tutorial, we will introduce a comprehensive overview of cross-domain image generation. Specifically, we categorize the cross-domain image generation problem into two main sets of tasks, i.e., supervised cross-domain image generation tasks and unsupervised/self-supervised cross-domain image generation tasks. We then provide a detailed taxonomy of the cross-domain image generation based on the different ways of designing model architecture, model optimization and sources of information, such as few-shot image generation or multi-modal image generation.