Complex and important decisions are often faced with the condition of deep uncertainty. Deep uncertainty has brought difficulties and risks far more than general uncertainty to decision. Since the 21st century, the research on the decision analysis under deep uncertainty is becoming one of the new important direction in the field of decision analysis. Firstly, the current research on decision making under deep uncertainty is combed, the decision characteristics and difficulties under deep uncertainty are summarized. Four main methods are described and analyzed in several aspects including the origin and development, the core idea, the implementation steps, and the typical applications. Then, a case is studied. Finally, the future research directions are suggested.