The development of computer vision has led to the successful application of deep learning to image compression.. Unlike the conventional coding framework, Learned Image Compression (LIC)learned image compression (LIC) methods are built upon neural networks and optimized end-to-end with a unified loss function instead of individually tuning each module. In this way, LIC methods can achieve global optimization, have demonstrated outstanding rate-distortion (RD) performance, and exceed conventional codecs such as JPEG and BPG. This chapter provides a systematic study of LIC, which can be categorized into three types based on functionality: Lossless image compressionlossless image compression, Lossy image compressionlossy image compression, and generative image compression. Specifically, lossy image compression as a crucial technique is reviewed at both the framework and component levels. Numerous works are proposed to enhance lossy learned image compression in terms of transformation and entropy models, which will be thoroughly discussed in the core components subsection. Following that, Generative image compressiongenerative image compression, mainly for human perception, is reviewed as well. It can maintain the subjective perception at extremely low bit rates.