Big data is big news, and large companies in all sectors are making significant advances in their customer relations, product selection and development and consequent profitability through using this valuable commodity. Small and medium enterprises (SMEs) have proved themselves to be slow adopters of the new technology of big data analytics and are in danger of being left behind. In Europe, SMEs are a vital part of the economy, and the challenges they encounter need to be addressed as a matter of urgency. This paper identifies barriers to SME uptake of big data analytics and recognises their complex challenge to all stakeholders, including national and international policy makers, IT, business management and data science communities. The paper proposes a big data maturity model for SMEs as a first step towards an SME roadmap to data analytics. It considers the ‘state‐of‐the‐art’ of IT with respect to usability and usefulness for SMEs and discusses how SMEs can overcome the barriers preventing them from adopting existing solutions. The paper then considers management perspectives and the role of maturity models in enhancing and structuring the adoption of data analytics in an organisation. The history of total quality management is reviewed to inform the core aspects of implanting a new paradigm. The paper concludes with recommendations to help SMEs develop their big data capability and enable them to continue as the engines of European industrial and business success.