The beginning of this decade finds artificial intelligence, high performance computing (HPC), and big data analytics in the forefront of digital transformation that is projected to heavily impact various industries and domains. Among those, the maritime industry has the potential to overcome many shortcomings and challenges through innovative technical solutions that combine the aforementioned innovative technologies. Naval vessels and shipping in general, generate extremely large amounts of data, the potential of which remains largely untapped due to the limitations of current systems. Simultaneously, digital twins can be used for conducting complex simulations of vessels and their systems to improve efficiency, automate, and evaluate current and future performance. However, they require large amounts of real-time and historical data to simulate efficiently, as well as AI models and high-performance computing that will help the entire system run smoothly and be scalable to higher volumes of data and computation requirements. Integrating these technologies and tools in a unified system poses various challenges. Under this context, the current publication presents the high-level conceptual architecture of VesselAI, an EU-funded project that aims to develop, validate and demonstrate a novel holistic framework based on a combination of the state-of-the-art HPC, Big Data and AI technologies, capable of performing extreme-scale and distributed analytics for fuelling the next-generation digital twins in maritime applications and beyond, including vessel motion and behaviour modelling, analysis and prediction, ship energy system design and optimisation, unmanned vessels, route optimisation and fleet intelligence.