Intelligent transportation systems (ITSs) will be a major component of tomorrow's smart cities. However, realizing the true potential of ITSs requires ultra-low latency and reliable data analytics solutions that can combine, in real-time, a heterogeneous mix of data stemming from the ITS network and its environment. Such data analytics capabilities cannot be provided by conventional cloud-centric data processing techniques whose communication and computing latency can be high. Instead, edge-centric solutions that are tailored to the unique ITS environment must be developed. In this paper, an edge analytics architecture for ITSs is introduced in which data is processed at the vehicle or roadside smart sensor level in order to overcome the ITS latency and reliability challenges. With a higher capability of passengers' mobile devices and intra-vehicle processors, such a distributed edge computing architecture can leverage deep learning techniques for reliable mobile sensing in ITSs. In this context, the ITS mobile edge analytics challenges pertaining to heterogeneous data, autonomous control, vehicular platoon control, and cyber-physical security are investigated. Then, different deep learning solutions for such challenges are proposed. The proposed deep learning solutions will enable ITS edge analytics by endowing the ITS devices with powerful computer vision and signal processing functions. Preliminary results show that the proposed edge analytics architecture, coupled with the power of deep learning algorithms, can provide a reliable, secure, and truly smart transportation environment.