Abstract: Flexible DC distribution systems mostly use power electronic equipment to interconnect with AC systems and accommodate distributed generators and loads. It has characteristics of low inertia and weak damping, and is easy to induce oscillations and instability with different frequencies by the random fluctuations of distributed generators and loads. This paper analyzes the challenges faced by stability analysis and control of flexible DC distribution system, and points out that its multi-time scale and stochastic characteristics are the main technical problems. By summarizing the research status of modeling, oscillation mechanism, stability analysis and control, the key research issues are prospected, including multi-time scale modeling, oscillation mechanism, stochastic disturbance stability analysis and robust stability control in multiple scenarios. The illuminated general framework is expected to bring more insights for the stability research of flexible DC distribution system.