In this paper, we reflect on how the principle of the ‘right to be forgotten’ (RTBF), specifically the right to erasure as enshrined in Article 17 (and to some extent Art. 19 and Art. 21) of the General Data Protection Regulation (GDPR; Regulation (EU) 2016/679), or the right to delete undesirable, unflattering or reputation‐damaging archived records of oneself from search engines or databases, might apply to academic publishing. In particular, we focus on archival (library and information) science, post‐publication peer review, and reflect on whether RTBF is compatible with open science principles. Even though RTBF became enshrined in EU law in 2018, its trans‐Atlantic export to the United States faces resistance because it is seen as being incompatible with First Amendment rights. We ponder the pertinence of the debate regarding local versus global applicability of RTBF when considering the transnational nature of some collaborative research. Although RTBF applies broadly to search engines such as Google, we question whether authors have this right and also whether publishers are subjected to this law with respect to science databases, or even ‘local’ (i.e., publisher‐controlled) archives, especially in the light of retractions or withdrawals, in which data and files are removed from a preprint or journal's website or, in extreme cases, where all or most bibliometric information is scrubbed clean, as in the case of ‘silent retractions’. We extend our reflections further to appreciate whether authors or editors are entitled to RTBF in extreme instances of misconduct or fraud. The fundamental right to privacy and personal choice, as is suggested by (or enshrined in) RTBF, is not—in our view—compatible with several principles related to the integrity of data and information, or even their preservation, and may be diametrically opposed, depending on the situation. We encourage wider debate on this budding pertinent issue as a fundamental aspect of academic rights and freedoms.