The Physical Internet (PI) is a novel, comprehensive and long-term vision of the future global freight transport and logistics (FTL) system, which is aimed at radically improving its efficiency and sustainability. As research on the PI concept is still young, the functioning of maritime ports in the context of the PI is still underexplored. Our aim is to contribute to the scientific debate about radically different futures for maritime ports around the world, by identifying their possible future development paths towards the PI. We construct an evolutionary port development framework that identifies the main dimensions of the PI in relation to ports, including governance, operational, and digital aspects. To design the future development paths towards the PI, we conducted a scenario analysis and used a Delphi survey amongst port development and PI experts. The resulting expectation is that a fully globally functioning of the PI may not be reached by 2040. Also, our analysis shows that global governance of FTL systems is critical for the pace of development and adoption. Building on the identified potential future development paths, we provide a discussion, relevant for port authorities and other stakeholders, as well as avenues for future research.