This chapter summarizes how the right not to know emerged during the 1980s and 1990s. It illustrates how this right has been politically and legally recognized and how it corresponds with actual social practices of not wanting to know one’s genetic traits. The chapter exemplarily discusses the discursive and argumentative contestation of the right not to know, mainly referring to an often-cited paper written by British ethicists John Harris and Kirsty Keywood in 2001. Using the example of novel technologies for preconception genetic carrier screening of (potentially all) couples planning to have children, the chapter then points to the ongoing dynamics of biomedical knowledge production which exerts considerable pressure on the right to ignorance as well as on social practices of not-knowing one’s genetic dispositions. The right to ignorance is frequently countered by claims of a “duty to know” in the name of genetic solidarity and responsibility.