There has been a huge increase in the number of social science surveys conducted over the Internet in the last decade, especially in the area of quantitative research. Interest in this method has generated abundant literature, almost all of it in English-speaking world. The present article provides an exhaustive list of the questions raised in the literature by this survey method. They fall into two categories: issues relating to sampling procedures (who exactly responds to Web surveys?) and concerns about effects of the survey mode (what is the quality of responses elicited by Web surveys?). While there is consensus in one or two areas, researchers’ analyses are otherwise widely divergent. Many agree that random sampling is extremely difficult to achieve over the Internet, but the procedures used to compensate for sampling bias (weighting, post-stratification, propensity score adjustment) are strongly contested. Similarly, regarding the use of new technologies for innovative questionnaire design, studies demonstrating real and reproducible effects are still few and far between. The present article, which also cites examples of good practice, concludes by setting out the vital precautions to taken when designing a Web survey for social science research.