Vacancies of the crystal is one of the core issues in solid physics, solid state chemistry, metallurgy and materials science. In this paper, we present the latest research on the vacancy formation energy and size dependence of vacancy formation energy. According to the vacancy formation energy of common methods and common description of the vacancy formation energy theory, the vcancy formation energy characterization, calculation and simulation methods are described; the nature and origin of the vacancy in nanoscale is analyzed. finally, further research will focus on the properties mechanisms of the other physical properties, mechanical properties and thermodynamic in materials.