The possibility of conducting surveys over the Internet has significant appeal, not least because of the advantages it offers in terms of cost-savings and the speed with which data can be collected from large samples. Yet a major barrier, which has prevented its widespread take-up in the context of large-scale general population surveys is the challenge of convincing people to answer questionnaires online. Nonresponse is a growing problem in survey research generally (e.g. Brick and Williams, 2013), but web surveys frequently suffer from lower response rates than can typically be achieved using other survey modes (Manfreda et al., 2008). This has led to concerns that moves to web-based data collection may reduce overall survey quality due to an increase in non-response bias. In this paper, I examine the main participation and engagement challenges for different types of survey design in which web might be incorporated, review some relevant studies, and identify opportunities for new research.