In recent years, it was found that antiperovskite compounds Mn3AX(A=Cu, Zn, Sn, Ni, Al, Ga etc.;X=N/C) exhibit abundant physical properties. Their useful functionalities arising from the interplay between crystal lattice and magnetism, such as superconductivity, giant magnetoresistance, near-zero temperature coefficient of resistance, negative thermal expansion, magnetostriction, piezomagnetic effect, the magnetocaloric effect, etc, have aroused the great interest. The thorough study of the crystal structure and physical properties of Mn3AX is important for understanding the relationship of "nature-structure". In this article, we review the progress in the peculiar physical properties of Mn3AX, especially the progress of strong correlations among lattice, electronic transport and magnetic ordering. Meanwhile, the control over the lattice,magnetoresistance and magnetic transition is also reviewed. Finally, some perspectives are proposed.