Metamaterial, as a groundbreaking artificial material, plays a revolutionary role in the field of electromagnetic wave control. A combination of transformation optics with metamaterials can not only give full play to the wonderful properties of metamaterials and realize many magical effects but also be applied to optical simulation, displaying some cosmological phenomena that cannot be observed directly. However, due to the limitation of the metamaterial structure, some electromagnetic parameters cannot be controlled by the microstructure, and then curved surfaces start to attract attention of people. It has been found that waveguides with curved structures can also regulate electromagnetic waves and break through some limitations of metamaterials to achieve many novel effects. By introducing a series of work on curved waveguides by research group of Liu Hui in Nanjing University, the wonderful applications of curved waveguides in various directions are demonstrated, and the application prospects of curved waveguides are discussed.