Abstract: With the increasing proliferation of distributed energy resources in the distribution network, how to establish an effective market-based trading mechanism in the power distribution and consumption system, while achieving efficient and coordinated optimization of market trading and power system operation has attracted unprecedented research interests in China and beyond. In the market environment, the operation and management of each layer of the power distribution and consumption system face multiple challenges, including the layer-wise increasing uncertainties, the increasing scale of market transactions, and lack of efficient coordination of market trading and safe operation of the system. This paper firstly outlines the critical scientific problems associated with optimal operation of power distribution and consumption systems in a market environment. Second, it critically reviews and summarizes existing research efforts in this area, employing conventional optimization-based solution techniques, and subsequently concludes remaining issues that deserve further research attention. Going further, this paper comprehensively reviews relevant deep reinforcement learning techniques and outlines their current applications in the examined research area, considering the primary characteristics pertaining to market trading and dispatch challenges associated with distribution and consumption system. Finally, this paper details three directions which require further research efforts, and also dives deep in revealing how deep reinforcement learning techniques can be developed and extended to support relevant research activities.