Integrated microcombs bring a parallel and coherent optical frequency comb to compact chip-scale devices. They offer promising prospects for mass-produced comb sources in a compact, power-efficient, and robust manner, benefiting many basic research and practical applications. In the past two decades, they have been utilized in many traditional fields, such as high-capacity parallel communication, optical frequency synthesis, frequency metrology, precision spectroscopy, and emerging fields like distance ranging, optical computing, microwave photonics, and molecule detection. In this review, we briefly introduce microcombs, including their physical model, formation dynamics, generation methods, materials and fabrications, design principles, and advanced applications. We also systematically summarize the field of integrated optical combs and evaluate the remaining challenges and prospects in each aspect.