This paper presents a critical review of the research conducted for modeling and controlling supercritical power plants. Thermal power plants are classified according to the boiler pressure to supercritical and subcritical. The modeling concepts and control strategies of supercritical generation units are far more complex than those of subcritical. On the other hand, supercritical generation technologies are more efficient and much cleaner than subcritical generation units. From a deep technical analysis of the literature, there is no review that is dedicated to models-based control of supercritical power plants and most previous reviews are found to be too general to modeling-based control of fossil fuelled energy sources. This review reports the advancements on modeling and control of supercritical and ultra-supercritical plants as cleaner generation technologies. The various published achievements for modeling supercritical and ultra-supercritical units have been reviewed. The control strategies that fulfill the practical load demand requirements while keeping optimum efficiencies are also reviewed. Finally, expected future directions are reported as recommendations to overcome future challenges. The paper can be used as a brief educational directory to the postgraduate students or future researchers in the field.