Connected Vehicles and Autonomous Vehicles (CAVs) provide various sources of vehicular related information to intersection infrastructure by integrating on-board sensors processing, wireless communication and other Vehicle-to-Infrastructure (V2I) technologies. Thus connected vehicle technologies can potentially remedy data collection limitations of existing urban intersection managements, enhancing the performances of intersection controls such as reducing vehicle delay, reducing vehicle number of stops and improving energy efficiency. This paper reviews optimization-based signal controls for different penetrations of connected vehicles and conventional vehicles environments, autonomous intersection management specific to completely 100% AVs road states, as well as signal-trajectory joint control for different adoptions of conventional vehicles, CVs and AVs mixture environments. Real time data processing, signal timing optimizations, vehicle trajectory motion planning and evaluation frameworks are summarized to highlight the advantages and limitations of respective intersection control paradigms. It is important to recognize that realistic scenarios in comparative assessments for proposed methods need to be achieved in future works. The effectiveness of different approaches is challenging to be compared without complete evaluation frameworks, and sensitivity analysis and hypothesis tests involving variety penetration rates and flow demands should be performed in order to test the stability of methods in different scenarios.