Increasing containerization and competition among seaport container terminals have become quite remarkable in worldwide international trade. Operations are nowadays unthinkable without effective and efficient IT use and appropriate optimization (management science and operations research) methods. Besides enabling efficient data interchange between supply chain partners, related information systems need to support terminal operators, shipping companies and even port authorities. We describe and classify the main logistics processes and operations in container terminals and survey methods for their optimization. Moreover, we extend towards recent challenges going beyond pure operations but extending to global competition on various levels.