Eco-driving is adopting an eco-conscious driving style with the potential to reduce fuel consumption in an easy and cost-effective way. This dissertation develops a methodology to calculate the most fuel-efficient driving behavior. Eco-driving is treated as an optimal control problem. Different low-degree quasistatic polynomial fuel consumption models and optimal control methods are evaluated. The proposed methodology uses quadratic fuel consumption models and Pontryagins maximum principle. An explicit and comprehensive expression for the optimal engine control is derived. Gear shifting is introduced by maximizing or minimizing an additional variable. Simulations reveal some interesting properties of optimal driving behavior. These results are used to propose refined eco-drive guidelines.