Connected and Autonomous Vehicles (CAVs) benefit from both connectivity between vehicles and city infrastructures and automation of vehicles. In this respect, CAVs can improve safety and reduce traffic congestion and environmental impacts of daily commutes through making collaborative decisions. This dissertation studies how to reduce the energy consumption of vehicles and traffic congestion by making high-level routing decisions of CAVs. The first half of this dissertation considers the problem of eco-routing (finding the energy-optimal route) for Plug-In Hybrid Electric Vehicles (PHEVs) to minimize the overall energy consumption cost. Several algorithms are proposed that can simultaneously calculate an energy-optimal route (eco-route) for a PHEV and an optimal power-train control strategy over this route. The results show significant energy savings for PHEVs with a near real-time execution time for the algorithms. The second half of this dissertation tackles the problem of routing for fleets of CAVs in the presence of mixed traffic (coexistence of regular vehicles and CAVs). In this setting, all CAVs belong to the same fleet and can be routed using a centralized controller. The routing objective is to minimize a given overall fleet traveling cost (travel time or energy consumption). It is assumed that regular vehicles (non-CAVs) choose their routing decisions selfishly to minimize their traveling time. A framework is proposed that deals with the routing interaction between CAVs and regular uncontrolled vehicles under different penetration rates (fractions) of CAVs. The results suggest collaborative routing decisions of CAVs improve not only the cost of CAVs but also that of the non-CAVs. This framework is further extended to consider congestion-aware route-planning policies for Autonomous Mobility-on-Demand (AMoD) systems, whereby a fleet of autonomous vehicles provides on-demand mobility under mixed traffic conditions. A network flow model is devised to optimize the AMoD routing and rebalancing strategies in a congestion-aware fashion by accounting for the endogenous impact of AMoD flows on travel time. The results suggest that for high levels of demand, pure AMoD travel can be detrimental due to the additional traffic stemming from its rebalancing flows, while the combination of AMoD with walking or micromobility options can significantly improve the overall system performance.