Background: The reported data on European universal neonatal hearing screening (UNHS) practices tend to be scarce, despite the fact that the European Union project, EUScreen, collected unofficial data from 38 collaborating European institutions. The objectives of this systematic review were as follows: (a) to identify the most recent (in a 20-year span) literature information about UNHS programs in Europe and (b) to provide data on the procedures used to assess the population, the intervention policies, and on the estimated prevalence of congenital hearing loss with emphasis on the bilateral hearing loss cases. Methods: Queries were conducted via the Pubmed, Scopus and Google Scholar databases for the time period of 2004–2024. The Mesh terms used were “OAE”, “Universal Neonatal Hearing Screening”, “congenital hearing loss” and “well babies”. Only research articles and review papers of European origin were considered good candidates. The standard English language filter was not used, in order to identify information from non-English-speaking scientific communities and groups. Results: Very few data and reports were identified in the literature search. Eleven manuscripts were identified corresponding to eight UNHS programs. Except in Poland, most of the data refer to regional and not national programs. The screening coverage estimates of all programs exceed 90%; infants were mostly assessed by a three-stage protocol (TEOAE + TEOAE + AABR), followed by a clinical ABR test. The average prevalence (i.e., from well babies AND NICU infants) of bilateral hearing loss ranged from 0.5 to 20.94 per 1000 (Zurich sample). Infants presenting unilateral or bilateral hearing losses were first rehabilitated by hearing aids and consequently (>15 mo) by cochlear implants. Conclusions: Even though UNHS programs are well-established clinical practices in the European States, the amount of information in the literature about these programs is surprising low. The existing data in the timespan 2004–2024 corroborate the international UNHS data in terms of coverage and bilateral hearing loss prevalence, but there is a strong need to supplement the existing information with the latest developments, especially in the area of hearing loss rehabilitation.