Abstract: The conformal transformation is a very important analytical method based on analytic functions. It can be used to transform the complex boundary in the virtual space into a simple one in the physical space to solve the two-dimensional planar field problem. This paper mainly reviews and introduces the application of conformal transformation in geometric optics. Numerous electromagnetic devices such as perfect invisibility cloaks, relay lenses, waveguide bends and lens antennas can be designed by controlling light propagation. Finally, the design is proved by ray tracing simulation and full wave simulation.