Connected and automated vehicles (CAVs) have the potential to address a number of safety, mobility, and sustainability issues of our current transportation systems. Cooperative longitudinal motion control is one of the key CAV technologies that allows vehicles to be driven in a cooperative manner to achieve system-wide benefits. In this paper, we provide a literature survey on the progress accomplished by researchers worldwide regarding cooperative longitudinal motion control systems of multiple CAVs. Specifically, the architecture of various cooperative CAV systems is reviewed to answer how cooperative longitudinal motion control can work with the help of multiple system modules. Next, different operational concepts of cooperative longitudinal motion control applications are reviewed to answer where they can be implemented in today's transportation systems. Different cooperative longitudinal motion control methodologies and their major characteristics are then described to answer what the critical design issues are. This paper concludes by describing an overall landscape of cooperative longitudinal motion control of CAVs, as well as pointing out opportunities and challenges in the future research and experimental implementations.