Spin-orbit coupling (SOC) is a bridge between the spin and orbital of an electron. Through SOC, spin of the electron can possibly be controlled throuth external electric fields. It is found that many novel physical phenomena in solids are related with SOC, for example, the magnetic anisotropy of magnetic materials, the spin Hall effect, and the topological insulator, etc. In the surface of solid or at the interface of heterostructure, Rashba SOC is induced by the structure inversion asymmetry. It was observed first in semiconductor heterostructure, which has an inversion asymmetric potential at the interface. Because Rashba SOC at the interface can be easily controlled through gate voltage, it is of great significance in the field of electric control of magnetism. Metal surface subsequent to semiconductor becomes another main stream with large Rashba SOC. In this paper, we review the recent progress in Rashba SOC in metal surfaces, including both the magnetic and nonmagnetic metal surfaces. We demonstrate the findings in Au(111), Bi(111), Gd(0001), etc., and discuss the possible factors that could influence Rashba SOC, including the surface potential gradient, atom number, the symmetry of the surface wavefunction, and the hybridization between the different orbitals in the surface states, etc. We also discuss the manipulation of Rashba SOC through electric field or surface decoration. In addition, on magnetic surface, there coexist Rashba SOC and magnetic exchange interaction, which provides the possibility of controlling magnetic properties by electric field through Rashba SOC. The angle-resolved photoemission spectroscopy and the first-principles calculations based on density functional theory are the two main methods to investigate the Rashba SOC. We review the results obtained by these two approaches and provide a thorough understanding of the Rashba SOC in metal surface.