In the middle of last century, some scientists discovered grain-boundary anelastic relaxation (GAR) peaks by means of torsional pendulum. Later, various models about the origin of GAR peaks are established through further research. However, its micro-mechanism is still unclear. Recently, according to the results of solute grain boundary segregation or dilution caused by elastic stress, a micro-mechanism of GAR which is grain-boundary absorbing or emitting vacancies has been proposed. Then, the equilibrium equations and the kinetic equations of GAR are established, and the process of GAR is expressed analytically. Furthermore, it has successfully elaborated the intermediate temperature embrittlement peak movement which exists widely in metals. Those developments of GAR theory are reviewed in the present paper.