Abstract: It is 100 years since thewell-know Mohr-Coulomb strength theory was established in 1900. Aconsiderable amount of theoretical and experimental research on strengththeory of materials under complex stress state was done in the 20thCentury. This review article presents a survey of the advances instrength theory (yield criteria, failure criterion, etc) of materials(including matellic materials, rock, soil, concrete, ice, iron,polymers, energetic material, etc) under complex stress, discusses therelationship among various criteria, and gives a method of choosing areasonable failure criterion for applications in research andengineering. Three series of strength theories, the unified yieldcriterion, the unified strength theory, and others are summarized. Thisreview article contains 1163 references regarding the strength theories. This review also includes a biref discussion of the computational implementation of the strength theories and multi-axial fatigue.