Vehicular ad hoc networks (VANETs) have become a hot research area over the past few years. The main purpose of VANETs is to improve traffic safety, traffic efficiency, and driving comfort. Particularly, traffic safety attracts the great attention of government, academia, and industry, because it is the most critical aspect of VANETs related to human lives. Therefore, many safety applications in VANETs have been proposed and investigated. However, how to guarantee the reliability of safety applications in VANETs is a big challenge, considering its natures of vehicle mobility and ad-hoc connection. In this paper, we provide an overview of VANETs for safety applications. Then, we discuss the specific reliability requirements in VANETs and the corresponding quality of service (QoS) metrics. Furthermore, based on these requirements and metrics, we analyse and evaluate whether or not current VANETs are able to support safety applications with stringent reliability requirements. New insights into potential enhancements from perspective of both new dynamic QoS requirements and radio resource sharing are provided and discussed. Finally, we illustrate future research directions to improve the reliability of VANETs for safety applications.