It is clear from the singularity theorem that the formation of black holes is inevitable in the Universe, but the path from massive stars to black holes cannot be “smooth” under their own gravity. By analyzing the balance between the internal and gravitational energy of stars, the process from main sequence star to compact star (white dwarf, neutron star and black hole) is discussed in general, and the semi-quantitative relationship between the accumulated internal energy per baryon (ε) and the stellar radius (R) is also presented. During a stars journey towards the singularity (R→0), there are three stages that prevent it from gravitational collapse, corresponding to the internal energy per baryon of ε ~keV(main-sequence stars), ~MeV (white dwarfs) and ~100 MeV (neutron stars). For black holes，R→0, ε→∞. Finally, the basic physical properties of compact stars and their impact on the modern astrophysics, as well as the education of stellar astronomy, are briefly reviewed.