This paper presents various aspects of atmospheric refraction to gain insight into the advances in this field. It divides the effects of atmospheric refraction into two categories: the visible-to-infrared bands used in research fields such as optical imaging, laser transmission, and optoelectronic tracking and the radio band used in radar measurements and satellite detection. The calculation formulas for these two bands are different in their practical treatment. This paper introduces the refractive index formulas according to the refractive index formula's development history and points out the limitations of each formula. The current best choice for the former formula is the one summarized by Rüeger scholars; for the latter, it is recommended to choose the radio refractive index formula in the Rec. ITU-R P.453-14. In addition, the relationship between the refractive index of the Earth's surface and altitude, reference data for the refractive index on a global scale, and statistical distributions for the calculation of the refractive index gradient are given in the recommendation. Finally, traditional calculation methods for obtaining atmospheric refraction and optical observation methods are presented. The former study is based on the modeling of atmospheric patterns or meteorological data, formulae for refractive indices in specific regions, or model fitting to satisfy accuracy in a single environment or on an average scale. The optical measurement method does not need an atmospheric model as a basis, nor does it rely on meteorological parameters. The measurement results of the data are real-time and more representative of the path. It can make up for some of shortcomings of the traditional methods, and is more in line with future development trend of the future.