Sensors are essential for the intelligence needed by smart cities, particularly smart transportation applications, and have been increasingly deployed over the past decade. Although these sensors are capable of collecting a substantial amount of data, the bandwidth and cost constraints of the communication network may not allow all these data to be transferred for timely processing on the cloud or server. Thus it is highly desirable to process, store, and extract data at the edge where things and people produce or consume the data, and this has led to a new research field called edge computing. Due to the limited computing power at the edge devices (such as the sensors), however, conventional computation models, particularly artificial intelligence (AI) methods, cannot be directly applied. To address this challenge, research efforts are needed to develop new methods and tools for efficient data processing, analysis, and understanding. This talk intended to introduce a couple of such research efforts made at the University of Washington Smart Transportation Applications and Research Laboratory (STAR Lab) that produced example edge computing methods, including edge AI, for safer and smarter transportation applications. The superb performance of these edge computing methods clearly indicates the value of such research efforts. Hopefully, this presentation will stimulate more researchers to invest their energy in edge computing methods and tools for improved transportation safety and system operations.