Structural discontinuities (e.g., nozzle, hole, and groove) widely occur in many high temperature components of nuclear and fossil power plants. In general, the notched component is used for simplified tests and analyses due to the complexity of the introduction of a practical component. In the previous work, the effects of the notch on failure life of the components have been reported experimentally, including the strengthening and weakening effects; however, the internal mechanisms have not been clearly demonstrated. This work reviews the notch effects on the structural strength of the notched components at elevated temperatures under creep, fatigue, and creep-fatigue loading conditions. Experimental phenomena (i.e., strengthening or weakening effects) for typical notched specimens subjected to the above three loading conditions are summarized, and the related factors for notch effects on creep rupture life or cycle to failure of the components are discussed. The mechanisms for the strengthening or weakening effects induced by a notch are described. Evaluation procedures for notch effect analysis under complex loading conditions are also included, and the primary challenges concerning the notch effect are provided for further investigations.