Autonomous driving is delightedly an innovative and revolutionary paradigm for future intelligent transport systems. To be fully functional and efficient, vehicles will use hundreds of sensors and generate terabytes of data that will be used and shared for safety, infotainment and allied services. Communication among vehicles or between vehicle and infrastructure thus requires data rate, latency and reliability far beyond what the legacy dedicated short-range communication (DSRC) and long-term evolution-advanced (LTE-A) systems can support. In this work, the authors motivate the use of millimetre-wave (mmWave) massive multiple-input multiple-output (MIMO) technology to facilitate gigabits-per-second (Gbps) communication for cellular vehicle-to-infrastructure scenarios. As a fundamental component, the authors characterise the mmWave massive MIMO vehicular channel using metrics such as path loss, root-mean-square delay spread, Rician K-factor, cluster and ray distribution, power delay profile, channel rank and condition number as well as data rate. They compare the mmWave performance with the DSRC and LTE-A capabilities, and offer useful insights on vehicular channels. The results show that mmWave massive MIMO can deliver Gbps data rates for next-generation vehicular networks.