With the rapid development of communication technology, connected vehicles (CV) have the potential, through the sharing of data, to enhance vehicle safety and reduce vehicle energy consumption and emissions. Numerous research efforts are quantifying the impacts of CV applications, assuming instant and accurate communication among vehicles, devices, pedestrians, infrastructure, the network, the cloud, and the grid, collectively known as V2X (vehicle-to-everything). The use of cellular vehicle-to-everything (C-V2X), to share data is emerging as an efficient means to achieve this objective. C-V2X releases 14 and 15 utilize the 4G LTE technology and release 16 utilizes the new 5G new radio (NR) technology. C-V2X can function without network infrastructure coverage and has a better communication range, improved latency, and greater data rates compared to older technologies. Such highly efficient interchange of information among all participating parts in a CV environment will not only provide timely data to enhance the capacity of the transportation system but can also be used to develop applications that enhance vehicle safety and minimize negative environmental impacts. However, before the full benefits of CV can be achieved, there is a need to thoroughly investigate the effectiveness, strengths, and weaknesses of different CV applications, the communication protocols, the varied results with different CV market penetration rates (MPRs), the interaction of CVs and human driven vehicles, the integration of multiple applications, and the errors and latencies associated with data communication. This paper reviews existing literature on the environmental, mobility and safety impacts of CV applications, identifies the gaps in our current research of CVs and recommends future research directions.