The MAX phases are a group of layered ternary compounds with the general formula M n+1 AX n (M: early transition metal; A: group A element; X: C and/or N; n = 1-3), which combine some properties of metals, such as good electrical and thermal conductivity, machinability, low hardness, thermal shock resistance and damage tolerance, with those of ceramics, such as high elastic moduli, high temperature strength, and oxidation and corrosion resistance. The publication of papers on the MAX phases has shown an almost exponential increase in the past decade. The existence of further MAX phases has been reported or proposed. In addition to surveying this activity, the synthesis of MAX phases in the forms of bulk, films and powders is reviewed, together with their physical, mechanical and corrosion/oxidation properties. Recent research and development has revealed potential for the practical application of the MAX phases (particularly using the pressureless sintering and physical vapour deposition coating routes) as well as of MAX based composites. The challenges for the immediate future are to explore further and characterise the MAX phases reported to date and to make further progress in facilitating their industrial application.