Road freight transport is one of the sectors with the highest greenhouse gas emissions and fuel consumption in the logistics industry. In recent years, due to the increase in carbon dioxide emissions, several companies have considered reducing them in their daily logistics operations by means of better routing management. Green vehicle routing problems (GVRPs) constitute a growing problem direction within the interplay of vehicle routing problems and environmental sustainability that aims to provide effective routes while considering environmental concerns. These NP-hard problems are one of the most studied ones in green logistics, and due to their difficulty, there are many different heuristic and hybrid techniques to solve them under the need of having high-quality solutions within reasonable computational time. Given the role and importance of these methods, this review aims at providing a comprehensive overview of them while reviewing their defining strategies and components. In addition, we analyze characteristics and problem components related to how emissions are being considered. Lastly, we map and analyze the benchmarks proposed so far for the different GVRP variants considering emissions.