With the development of display technology, the demand for high-performance and high-stability thin film transistors (TFTs) is increasing. The method of improving the performance of thin film transistors through crystallization has received a lot of attention. Currently, indium gallium zinc oxide (IGZO) materials are widely used in the channels of thin film transistors due to their advantages such as high mobility, flexibility, and high transparency. Improving the crystalline morphology of the IGZO channel layer has become a research hotspot. This article summarizes the research progress of crystalline IGZO thin film transistor devices, introduces in detail the crystal structure of IGZO compounds, and focuses on the structure of single crystalline, c-axis-aligned crystalline, hexagonal polycrystalline, spinel, nanocrystalline, and protocrystalline IGZO, as well as the preparation methods, device performance, and stability of various crystalline IGZO thin-film transistors. We also analyze the microstructure of crystalline IGZO, summarize the physical properties, describe the crystallization mechanism and establish the relationship between crystal structure and electrical properties. At last, the development of crystalline IGZO thin film transistor is prospected.