Abstract: Due to its unique layered structure and special chemical bonding between atoms, MAX phase ceramic materials (chemical formula M_n+1AX_n) have excellent properties of both metal and ceramic materials. These excellent properties make them a promising material in many fields. Since its discovery in the 1960s, it has been paid more attentions. More than 100 MAX phases have been discovered, including more than 80 single phases and a series of solid solutions. The traditional MAX phases are limited to a certain range of elements and the structure in which M₆X layers and single A atomic layer are alternately stacked. The recent successful syntheses of MAX phases containing Au, Ir, Cu, Zn and other elements have largely enriched the MAX phase family. The discovery of multiple A layers and multiple MA layers MAX phases have also opened a door for new MAX phases. With the developments and applications of first-principles calculations and the progresses of modern experimental techniques, more and more new MAX phases have been predicted theoretically or synthesized experimentally. The recent advances on the experimental syntheses and theoretical researches of MAX phases based on new elements and new multilayer structures were summarized, and the problems that need to be overcome in the following researches were pointed out in this article. Finally in order to provide a useful reference for the future, the research directions and developing trends of the new MAX phases are prospected.

Key words: MAX phase ceramic material, MAX phase, MAX phases with new element, MAX phase with multilayer structure, MAX phases with multi-A layer, MAX phase with multi-MA layer, first-principle