Laser cooling of relativistic heavy ion beams at storage rings is one of the most promising techniques to reach high phase-space densities and achieve phase transition, ordered beam even crystalline beam. Compared with the established cooling schemes at storage rings, such as stochastic cooling and electron cooling, laser cooling has many advantages such as fast-cooling, ultra-strong cooling force and providing an ultra-low temperature (mK) ion beams. In addition, the precision laser spectroscopy of the highly charged ions can be performed by using the laser-cooled ion beams during the laser cooling experiments. We introduce the experimental principal and methods of laser cooling of relativistic ion beams at the experimental cooler storage ring of the CSRe at the Institute of Modern Phyics, Chinese Academy of Sciences. The first experimental results from a beam time aiming for laser cooling of 122 MeV/u Li-like ~(12)C~(3+) at the CSRe with a pulsed laser are presented, and laser cooling and precision laser spectroscopy of relativistic Li-like and Na-like highly charged ions at the future large facility HIAF and FAIR are outlined.