Vehicular Ad-hoc Network (VANET) is an emerging autonomous dynamic topology network. It is a special kind of Mobile Ad-hoc Network in which the vehicles exchange their information with each other. VANET turns every car in it into a mobile node and use these nodes to create a mobile dynamic network. The purpose of VANET is to supply a wireless connectivity and deploy various applications such as collision avoidance, safety and improving the traffic efficiency as provisioned by the Intelligent Transportation System (ITS). The vehicles are constrained by the realistic traffic environment, and now the simulations are mainly network simulations which cannot simulate the real trace of the vehicle. But as nodes in VANETS have very high mobility, so there are lots of challenges to route the packets to there final destination which need to be addressed by existing/proposing new solutions for the same. Keeping view of above, In this paper, We summarize the existing VANET routing protocols and classify and compare them. Then, We list several classic routing algorithms and analyze their characteristics and advantages and disadvantages. Finally, by analyzing the status quo of vehicle-mounted routing protocols, we illustrate the difficulties and challenges that vehicle-mounted routing protocols will encounter in the future.