A review with 181 refs. The acceptance of microwave digestion technique is based on procedures successfully carried out for most sample types. It is not only the knowledge of the mechanism of microwaves interaction with the material scientists deal with but more the exptl. procedures for the most efficient reagent attack. The goals of this paper are to gather all information concerning application of microwave digestion methods for elemental anal. and to review the results obtained by selecting several groups of materials digested.