When economists talk about ‘measurement’ they tend to refer to metrics that can capture changes in quantity, quality and distribution of goods and services. In this paper we argue that the digital transformation of the economy, particularly the rise of cloud computing as a general-purpose technology, can pose serious challenges to traditional concepts and practices of economic measurement. In the first part we show how quality-adjusted prices of cloud services have been falling rapidly over the past decade, which is currently not captured by the deflators used in official statistics. We then discuss how this enabled the spread of data-driven business models, while also lowering entry barriers to advanced production techniques such as artificial intelligence or robotic-process-automation. It is likely that these process innovations are not fully measured at present. A final challenge to measurement arises from the fragmentation of value chains across borders and increasing use of intangible intermediate inputs such as intellectual property and data. While digital technologies make it very easy for these types of inputs to be transferred within or between companies, existing economic statistics often fail to capture them at all.