Major efforts are currently under way to develop e‐infrastructures for research. At the same time, there have been a number of calls for research in the digital realm to foster ‘openness’, for example in ‘open access’ policies. This paper explores the relation between e‐infrastructures and open science, and argues that there are a number of factors apart from research policy that will shape e‐research. These include not only the legal and economic environment, but also the ethos of science, ‘open’ initiatives outside of research, the momentum of large technological systems, and the activism of experts and wider social movements. The paper assesses the strengths and weaknesses of these factors, as well as the tensions and confluences between openness and e‐infrastructures.