With 5G mobile communication systems been commercially rolled out, research discussions on next generation mobile systems, i.e., 6G, have started. On the other hand, vehicular technologies are also evolving rapidly, from connected vehicles as coined by V2X (vehicle to everything) to autonomous vehicles to the combination of the two, i.e., the networks of connected autonomous vehicles (CAV). How fast the evolution of these two areas will go head-in-head is of great importance, which is the focus of this paper. Based on a brief overview on the technological evolution of V2X to CAV and 6G key technologies, this paper explores two complementary research directions, namely, 6G for CAVs versus CAVs for 6G. The former investigates how various 6G key enablers, such as THz, cell free communication and artificial intelligence (AI), can be utilized to provide CAV mission-critical services. The latter discusses how CAVs can facilitate effective deployment and operation of 6G systems. This paper attempts to investigate the interactions between the two technologies to spark more research efforts in these areas.