Green vehicle routing problem (GVRP) aims to consider greenhouse gas emissions reduction, while routing the vehicles. It can be either through adopting Alternative Fuel Vehicles (AFVs) or with existing conventional fossil fuel vehicles in fleets. GVRP also takes into account environmental sustainability in transportation and logistics. We critically review several variations and specializations of GVRP to address issues related to charging, pick-up, delivery, and energy consumption. Starting with the concepts and definitions of GVRP, we summarize the key elements and contributors to GVRP publications. Afterward, the issues regarding each category of green vehicle routing are reviewed, based on which key future research directions and challenges are suggested. It was observed that the main focus of previous publications is on the operational level routing decision and not the supply chain issues. The majority of publications used metaheuristic methods, while overlooking the emerging machine learning methods. We envision that in addition to machine learning, reinforcement learning, distributed systems, internet of vehicles (IoV), and new fuel technologies have a strong role in developing the GVRP research further.