One of the notoriously difficult problems in vehicular ad-hoc networks (VANET) is to ensure that established routing paths do not break before the end of data transmission. This is a difficult problem because the network topology is constantly changing and the wireless communication links are inherently unstable, due to high node mobility. In this paper we classify existing VANET routing protocols into five categories: connectivity-based, mobility-based, infrastructure-based, geographic-location-based, and probability-model-based, according to their employed routing metrics. For each category, we present the general design ideas and state of the art. Our objective is to attract more attention to the VANET routing problem and encourage more research efforts on developing reliable solutions.