Vehicular communications have attracted more and more attention recently from both industry and academia due to their strong potential to enhance road safety, improve traffic efficiency, and provide rich on-board information and entertainment services. In this paper, we discuss fundamental physical layer issues that enable efficient vehicular communications and present a comprehensive overview of the state-of-the-art research. We first introduce vehicular channel characteristics and modeling, which are the key underlying features differentiating vehicular communications from other types of wireless systems. We then present schemes to estimate the time-varying vehicular channels and various modulation techniques to deal with high-mobility channels. After reviewing resource allocation for vehicular communications, we discuss the potential to enable vehicular communications over the millimeter wave bands. Finally, we identify the challenges and opportunities associated with vehicular communications.