With the large-scale integration of distributed renewable generation (DRG) and increasing proportion of power electronic equipment, the traditional power distribution network (DN) is evolving into an active distribution network (ADN). The operation state of an ADN, which is equipped with DRGs, could rapidly change among multiple states, which include steady, alert, and fault states. It is essential to manage large-scale DRG and enable the safe and economic operation of ADNs. In this paper, the current operation control strategies of ADNs under multiple states are reviewed with the interpretation of each state and the transition among the three aforementioned states. The multi-state identification indicators and identification methods are summarized in detail. The multi-state regulation capacity quantification methods are analyzed considering controllable resources, quantification indicators, and quantification methods. A detailed survey of optimal operation control strategies, including multiple state operations, is presented, and key problems and outlooks for the expansion of ADN are discussed.