The substantial growth in the number of electric vehicles has significantly deepened the integration of power systems and urban transportation systems, bringing both opportunities and challenges. Research on power-transportation fusion is burgeoning. First, common traffic assignment models according to time scales and application conditions are categorized. On this basis, coupling architectures and modeling methods for power-transportation systems are summarized. Furthermore, effective algorithms for addressing the solving difficulties in power-transportation systems, including the model nonconvexity and nonlinearity, multi-agent participation, and uncertainty management, are introduced. Then, recent advances in key problems of power-transportation system such as expansion planning, economic operation, low-carbon operation, peer-to-peer trading, and emergency restoration are elaborated in detail. Finally, the key technologies of future power-transportation coupling systems in research objects such as shared electric vehicles, hydrogen fuel cell vehicles, and mobile charging stations, as well as in research methods such as data-driven and online optimization are analyzed and prospected