Bibliometrics is deeply transformed by open science. The unprecedented availability of bibliographic metadata, full text search and additional use metrics creates new opportunities for quantitative studies of scientific corpus. It also challenges the historical focus of bibliometrics on citation data from a few selected journals. New approaches aim to expand its scope to different uses and different publics, especially in regard to the social impact of research. As a field, bibliometrics has been strongly influenced by the first commercial infrastructure for academic publications. In the 1960s, the Science Citation Index laid the fundamental basis of a structured research program on bibliometrics, with a primary focus on citation data and citation network from esteemed English-speaking journals in STM. This selective approach made it possible to run one of the first search engines with the limited computing technologies of the 1960s and has proven to be a direct inspiration for the search algorithm of Google (the “pagerank”). Yet, it also introduces several performative biases, as journals excluded from index on various grounds (non-English language, non-STM research) also become in turn less visible. As bibliometric indicators have been increasingly used in research evaluation and management, it ultimately penalized a large range of scholarly output and harmed the diversity of scientific activities. The development of the web had an immediate impact on bibliometrics. While hyperlinks are analogous to citation data, their use is not limited to scientific publications and can be applied to any publications. Alternative labels like webometrics, infometrics or cybermetrics have attempted to redefine and expand bibliometric analysis to a larger variety of documents and digital objects. The open science movements had originally a mixed relationship to bibliometrics. Publications in open access were initially supposed to have a citation advantage due to increased visibility and bibliometric indicators have been commonly used as arguments in favor of a transition to open science. Yet, bibliometric indexes (like the impact factor of the h-index) have also contributed to secure the position of major commercial publishers and possibly delay the transition to open science. Alternative approaches of bibliometrics (the altmetrics) have aimed to reframe bibliometric indicators to better integrate the values and objectives of open science, by taking into account non-academic uses through log analysis or social data metrics. By the end 2020s, the field of bibliometrics itself underwent an open science revolution. With the opening of scientific data and metadata, commercial vendors like the Web of science are displaced by public and community-led initiatives like the Initiative for Open Citations or Wikidata. Major actors in bibliometrics have started to rethink their methods, their research identity and their relationship with the leading commercial database, and adopting the broader label of Quantitative Science Studies.