The orbital eccentricity is one of the key parameters to describe the orbit of celestial bodies, which can provide important clues to reveal their dynamical evolution, and thus help to understand their formation and evolution processes along with the physical mechanisms behind them. The continuous improvement of observational technologies enables us to explore the orbit of celestial bodies beyond the Solar System, i.e., from stellar systems to planetary systems. Focusing on the orbital eccentricity of celestial bodies, this paper reviews the progress in stellar systems (including the main sequence stars, brown dwarfs, and compact stars) and planetary systems (including gas-giants, low-mass exoplanets such as ``super-Earth'' and ``sub-Neptune''), and summarizes several similarities and issues among the investigations of orbital eccentricity under different scales. Finally, based on the ongoing and future astronomical facilities and missions, we discuss the future prospect on eccentricity studies of stellar systems, extrasolar planetary systems and even extrasolar satellite systems.