Power system scheduling mainly concerns economic optimization issues of the power system, which is also commonly known as the unit commitment (UC) problem. However, improper planning in the generation schedule may pose a negative impact on power system stability. Additionally, the trend of large-scale integration of renewable energy in the future power system brings critical challenges to power system stability. In consequence, it is necessary to integrate the stability constraints into power system scheduling. According to the classic classification of power system stability (i.e. voltage stability, frequency stability, and rotor angle stability), stability constraints can be constructed accordingly to guarantee system stability when solving UC problems, which ensures both the economic efficiency and technical feasibility of the UC solutions. This paper reviews typical stability constraints and how to apply these constraints in solving UC problems. Representative works are summarized to provide a guidance for addressing the stability constrained scheduling problems in the future power system operation.