MAX phase ceramics have a unique crystal structure in which MX sheets and A-element layers are alternately stacked, so that it has both the excellent characteristics of metal and ceramics. They exhibit high electrical and thermal conductivities, and are machinable. And at the same time, they are resistant to oxidation and corrosion, and elastic stiff. They are attracting more and more attention in the past 20 years with their potential widely applications. In this paper, some research work on MAX phase and MXenes materials are reviewed. Firstly, recent discoveries on the newly MAX phases and their preparation method are introduced. Then, from the physical-property perspective, the research progress on the elastic, electrical, thermal and magnetic properties and radiation resistance of typical MAX phases is reviewed. In addition, a further introduction of MXene, which is a two-dimensional derivative of MAX phases, and its synthesis, characterization, properties and its application in electrochemical energy storage and in catalysis is presented. Finally, important future research directions are discussed. These include charting the unknown regions in phase diagrams to discover new MAX phases, exploring their unknown special physical properties, studying 2D derivative MXene, as well as researching their synthesis, characterization, and potential applications.