Digital skills for FAIR and open science are a cornerstone of the European Open Science Cloud (EOSC)’s operations and future. An EOSC network of skilled professionals is essential to bring a culture change for sharing research outcomes, and to empower individuals and institutions to develop and maintain EOSC competences, skills and capabilities. The EOSC Skills and Training Working Group (WG) was formed in 2020 to identify a framework for building competence and capabilities for EOSC. The WG focused on four priority areas that form the major sections of this report: 1. Developing the next generation of FAIR and open science professionals: Presents a framework of all the EOSC actors (roles) in the EOSC ecosystem for whom skills and training is relevant. 2. Collaborating to enhance digital skills for FAIR and open science in Europe: Reviews organisational approaches to implement training activities and programmes, through the concept of competence centres. 3. Building a trusted and long-lasting and trusted knowledge hub of learning and training resources and related tools: Provides insights for an EOSC federated training catalogue as part of a sustainable training infrastructure that supports EOSC actors. 4. Influencing national open science policy for skills by supporting strategic leaders: Analyses the framing of digital skills required in EOSC in the wider European agenda for skills, to provide recommendations for Member States and Associated Countries on how to support EOSC in national skills policies and strategies.