The phase-field method has emerged as a method ofchoice for the description of microstructure evolutionand phase transitions in metallic materials. Following ageneral thermodynamic extremal principle a set of evolutionequations for the structural variables of the system, the socalled phase-fields, are derived. The paper reviews shortlythe historical and theoretical background of the multi-phasefieldmethod that is an extension of the classical phase-fieldmethod to multi-phase multi-component materials. Examplesare given from solidification, solid state transformations andgrain growth.