Eco-friendly navigation (a.k.a. eco-routing) finds a route from A to B in a road network that minimizes the greenhouse gas (GHG) emission or fuel/energy consumption of the traveling vehicle. As road transport is a major contributor to GHG emissions, eco-routing has received considerable research attention in the past decade, mainly on two research themes: (1) developing models to estimate emissions or fuel/energy consumption of vehicles; and (2) developing algorithms to find eco-friendly routes for a vehicle. There are some excellent literature reviews that cover the existing estimation models. However, there is no literature review on eco-friendly route-planning algorithms. This article fills this gap and provides a systematic literature review in this area. From mainstream online databases, we obtained 2,494 articles and shortlisted 76 articles using our exclusion criteria. Accordingly, we establish a holistic view of eco-routing systems and define five taxonomies of estimation models, eco-routing problems and algorithms, vehicle types, traffic, and road network characteristics. Concerning the taxonomies, we categorize and review the shortlisted articles. Finally, we highlight research challenges and outline future directions in this important area.