AbstractThis chapter presents a best practice framework for the operation of Big Data and Artificial Intelligence Centres of Excellence (BDAI CoE). The goal of the framework is to foster collaboration and share best practices among existing centres and support the establishment of new Centres of Excellence (CoEs) within Europe. The framework was developed following a phased design science process, starting from a literature review to create an initial framework which was enhanced with the findings of a multi-case study of existing successful CoEs. Each case study involved an in-depth analysis and a series of in-depth interviews with leadership personnel of existing CoEs.The resulting best practice framework models a CoE using open systems theory that comprises input (environment), transformation (CoE) and output (impact). The framework conceptualises the internal operation of the CoE as a set of high-level capabilities including strategy, governance, structure, funding, and people and culture. The core capabilities of the CoE include business development, collaboration, research support services, technical infrastructure, experimentation/demonstration platforms, Intellectual Property (IP) and data protection, education and public engagement, policy outreach, technology and knowledge transfer, and performance and impact assessment. In this chapter we describe the best practice framework for CoEs in big data and AI, including objectives, environment, strategic and operational capabilities, and impact. The chapter outlines how the framework can be used by a CoE to support its strategic direction and operational decisions over time, and how a new CoE can use it in the start-up phase. Based on the analysis of the case studies, the chapter explores the critical success factors of a CoE as defined by a survey of CoE managers. Finally, the chapter concludes with a summary.