As well known, more than 99% of the observable matter in the universe is plasma and the plasma astrophysics studies various physical processes and phenomena occurring in cosmic plasmas, from small-scale collective interaction processes and energy transforming mechanisms in particle kinetics to the state of large-scale structure of cosmic objects and their eruptive phenomena. The present paper reviews the important role of the plasma astrophysics in the development of the modern astronomy as well as the formation of the modern plasma cosmology based on the history of the cosmic evolution, the formation of large-scale structures, and eruptive phenomena of cosmic objects. In addition, the unique function of satellite in situ exploring researches in space plasmas to act as the natural laboratory for the plasma astrophysics is further elaborated.