Increasing freight volumes and challenging environments in seaports and container terminals worldwide require streamlined and reliable operations. Digital twins are seen as important drivers of the digitalization in seaports by providing a basis for higher transparency, control and data-driven decision making. In this context, however, the concept is rarely studied, and implementation issues are not comprehensively discussed. The paper presents an exploratory study of digital twins in seaports based on a literature review and case studies. The analysis reveals a standardization deficit for digital twin implementations, an inflationary and improper use of the term digital twin, and fields of research that need to be explored further. The application of optimization methods and the integration of simulation-based optimization in the field of seaports and container terminals is examined, due to its relevance for digital twins. Important lessons learned can be taken from the most advanced implementations, integrating simulations and emulations with optimization methods. An in-depth examination of multiple case studies and discussions with global port leaders yields valuable perspectives on the varied levels of digital twin implementations being applied today, including insights into the most advanced implementations currently being used in ports and container terminals. As a result of the analyses conducted, various research directions and a research agenda are presented.