With the integration of fluctuating renewable production into the electricity system, electric-drive vehicles may contribute to the resulting need for flexibility, given that the market conditions provide sufficient economic incentive. To investigate this, we consider the short-term management of electric vehicles in a market environment. From the perspective of vehicle operators participating in the electricity spot market, the problem is to optimally charge and discharge the vehicles in response to spot market prices. We consider the case of a vehicle owner who is a price-taker and that of a fleet operator who can influence prices. In both cases, we show how the problem is amenable to dynamic programming with respectively linear and quadratic costs. With discretization of the state space, however, the problem of fleet operation is prone to suffer from the curse of dimensionality and, therefore, we propose an ex ante vehicle aggregation approach. We illustrate the results in a Danish case study and find that, although optimal management of the vehicles does not allow for storage and day-to-day flexibility in the electricity system, the market provides incentive for intra-day flexibility.