The design of novel light beams and investigation of their propagation properties are important topics in optics, particularly for beams that are nondiffracting, self-accelerating, or self-repairing. The evolution of these beams in either free-space or a waveguide and their applications have attracted a significant amount of research. Although wave optics has been developed as a rigorous and self-consistent framework, it does not offer intuitive processes for solving optical wave propagation. However, geometrical optics, also known as ray optics, can provide an intuitive and understandable method for analyzing light beam propagation and constructing targeted beam shapes in addition to designing optical systems. With the development of modern geometrical optics, rays have extended their physical meaning and are widely used to characterize optical wave propagation. Furthermore, ray characterization can explain nondiffracting, self-accelerating, and self-repairing properties. In this work, beginning with the fundamental theory of geometrical optics, we review the development, applications, and recent advances of significance of ray in modern ray optics. Meanwhile, some typical beams, such as fundamental-mode Gaussian, non-diffraction, and Airy beams, as well as beams with spiral wavefronts and structured Gaussian beams, have been characterized and designed using rays. Lastly, some challenging problems and future research directions of geometrical optics are discussed.