As communication technology is developing at a rapid pace, connected vehicles (CVs) can potentially enhance vehicle safety while reducing vehicle energy consumption and emissions via data sharing. Many researchers have attempted to quantify the impacts of such CV applications and vehicle-to-everything (V2X) communication, or the instant and accurate communication among vehicles, devices, pedestrians, infrastructure, network, cloud, and grid. Cellular V2X (C-V2X) has gained interest as an efficient method for this data sharing. In releases 14 and 15, C-V2X uses 4G LTE technology, and in release 16, it uses the latest 5G new radio (NR) technology. Among its benefits, C-V2X can function even with no network infrastructure coverage; in addition, C-V2X surpasses older technologies in terms of communication range, latency, and data rates. Highly efficient information interchange in a CV environment can provide timely data to enhance the transportation system's capacity, and it can support applications that improve vehicle safety and minimize negative impacts on the environment. Achieving the full benefits of CVs requires rigorous investigation into the effectiveness, strengths, and weaknesses of different CV applications. It also calls for deeper understanding of the communication protocols, results with different CV market penetration rates (MPRs), CV- and human-driven vehicle interactions, integration of multiple applications, and errors and latencies associated with data communication. This paper includes a review of existing literature on the safety, mobility, and environmental impacts of CV applications; gaps in current CV research; and recommended directions for future research. The results of this paper will help shape future research for CV applications to realize their full potential.