Connected autonomous vehicle (CAV) technology has the potential to enable significant gains in energy economy (EE). Much research attention has been focused on autonomous eco-driving control enabled by various methods. In this study, the state of the literature on autonomous eco-driving control is reviewed, an overall systems' description of eco-driving control for a CAV is provided, and representative methods are evaluated comparatively against each other in simulation. Simulations are conducted using real-world traffic signal data and a validated future automotive systems technology simulator (FASTSim) model. Results indicate that an EE improvement in the range of 5%-15% is attainable depending on the method and cost function used. In this article it is shown that dynamic programming (DP) methods are most effective in improving EE but are significantly more computationally expensive than other methods. The genetic algorithm (GA) methods are shown to present the most potential in terms of EE improvement and run-time. Results also indicate that velocity-sensitive cost functions allow all the methods to perform better than pure acceleration minimization.