Substantial attention has been paid to the stoi-chiometric displacement models for solute retention (SDM-R) in liquid chromatography and adsorption (SDM-A) at surfaces since they were developed. The SDM has a strongly theoretical basis and has evolved to the point that it is widely applied in chemistry, biochemistry, molecular biology and biotechnology. This review introduces the history, recent developments, and new concepts relating to the SDM, including theory, mathematical expressions, and applications across a broad range of fields. Substantial attention has been paid to the stoi-chiometric displacement models for solute retention (SDM-R) in liquid chromatography and adsorption (SDM-A) at surfaces since they were developed. The SDM has a strongly theoretical basis and has evolved to the point that it is widely applied in chemistry, biochemistry, molecular biology and biotechnology. This review introduces the history, recent developments, and new concepts relating to the SDM, including theory, mathematical expressions, and applications across a broad range of fields.