As the digitalisation of the economy progresses, one of the changes in business models affecting statistics including GDP and trade data is the adoption of cloud computing services in place of fixed investment in computer and communications hardware and the development of own-account software. This rapidly growing phenomenon involves the detachment of the physical location of data and computing processes from their creation, ownership and use, potentially introducing transactions across national borders. In this paper, we construct price indices for cloud services in the UK, showing significant price declines both before and after adjusting for quality in the past few years. We discuss the conceptualisation of a volume measure for cloud services. We discuss the implications of cloud use by businesses for the interpretation of measured business investment, GDP and productivity growth, noting in particular the limitations of measuring total factor productivity through growth accounting, and the importance of double deflation when there are significant changes in the price of intermediate goods such as cloud services. We discuss also the implications for the interpretation of international trade statistics. Finally, we set out the requirements for official statistical surveys to be able to track cloud computing in the future.