Scholars have put high hopes on automated vehicle (AV) technologies in revolutionizing transportation system performance, including multiplying road way capacity and minimizing energy consumption. However, our study observed that existing production AVs exhibit comparable or even inferior performance compared with human-driven vehicles (HDV). To bridge the discrepancy and realize the full potential of AVs, we propose a roadmap of cooperative & automated transportation from optimal trajectory control in the ideal conditions through a cooperative control framework incorporating edge computing and machine learning under real-world constraints. The analysis of ideal conditions (e.g., pure AV with perfect information and control) reveals critical theoretical properties specifying feasible time-space ranges of AV movements. Combined with customized mathematical programming and control methods, these properties lead to efficient solutions (e.g., in milliseconds) to real-time optimal trajectory planning problems. These solutions serve as the building blocks for solving more realistic AV control problems (e.g., mixed with human drivers, considering different cooperation classes, with stochasticity and errors). Further, significant efforts have been made in developing hardware technologies and physical experiments with both reduced-scale and full-scale AV test facilities to transfer modeling results to physical applications and implementable systems.