Liquid crystal microlens arrays, as one of the basic optical elements, have the advantages of tunable focal length, compact structure, low power consumption and good stability. They have a wide range of applications in the field of micro-/nano-optics. After nearly 40-year development, the research on liquid crystal microlens arrays has become gradually matured. Liquid crystal microlens arrays with different structures and applications have emerged rapidly. Here, this review article briefly summarizes the three working principles of liquid crystal microlens arrays, and describes the recent research progress separately. The review focuses on the manufacturing process, structural characteristics and working principle of liquid crystal microlens. Particularly, liquid crystal microlens arrays based on refraction and diffraction principles are respectively discussed, involving microlens structures, liquid crystal alignment techniques, as well as their applications. Finally, the key issues and future development trends of liquid crystal microlens arrays are summarized.