International sea-freight container transportation has grown dramatically over the last years and container terminals represent nowadays a key actor in the global shipping network. Terminal managers have to face with an increasing competitiveness among terminals, which require more and more efficiency in container operations both along the quayside and within the yard: the objective is usually to minimize ships turnaround time, one of the main indicators of the terminal performance for the shipping companies. Moreover, the minimization of operational costs directly entails the achievement of competitive terminal fares, thus increasing the attractiveness for new customers. Operations research methods and techniques are therefore worth being used in optimizing terminal operations. In this work, we firstly give an overview of decision problems which arise in the management of a container terminal (e.g. berth allocation, quay crane scheduling, storage policies and strategies, transfer operations, ship stowage planning) and provide a review of recent papers in the OR literature. Then, starting from a collaboration with some of the busiest ports in Europe, we identify some critical issues: in particular, we discuss the impact that gate and transshipment operations have on the yard. We also focus on competition and cooperation issues among port market players and decision makers. Finally, we conclude by suggesting possible research tracks and open issues.