Abstract: With the increase of the penetration rate of electric vehicles (EVs), the impact of electric vehicle charging demands on the power system is also increasing. On the one hand, the uncoordinated charging loads may bring threats to the secure operation of the power system; on the other hand, with the mobility of the electric vehicles, the spatial flexibility of EVs' charging demands can provide the demand-side response services for the power system. Aiming at the on-the-road energy management problem of electric vehicles, this article focuses on the researches on the spatial flexibility of EVs from two aspects: the modeling methods and the dispatching methods. Then it introduces in detail the applications in large-scale electric vehicle charging scheduling, the optimization of charging navigation for single EV, and the operation optimization of shared fleets considering charging and relocation. The future directions of researches on spatial flexibility of EVs' charging demands are finally summarized and prospected.