In this tutorial, we will introduce the recent progress in generative image compression, which targets on learning a compression model effeciently storing images with low bitrates while producing perceptually high-fieldlity reconstructions. It has drawn increasing attention and made tremendous development in recent years because of better perceptual quality than traditional image compression algorithms at equal bitrates. We therefore conduct this tutorial of the analysis, methodology, and related applications of generative image compression to clarify the main progress the community has made. Specifically, we first briefly introduce the two most representative generative models, variational autoencoders (VAEs) and generative adversarial networks (GANs), applied for generative image compression. Second, we explore the developing area of generative image compression, including existing methods and potiential directions. In summary, our tutorial will cover latest works and the progress in community, which will help the audiences with different backgrounds better understand the recent progresses in this emerging research area.