The Web of Science Core Collection is a highly selective, abstract-indexed scientometric database, which currently includes more than 21 thousand scientific journals of all specialties published in 110 countries. The database contains three specialized indexes: Science Citation Index Expanded (SCIE), Social Sciences Citation Index (SSCI), Art and Humanities Citation Index (AHCI) and a multidisciplinary Emerging Source Citation Index (ESCI). Today there are 15 Ukrainian journals included in the SCIE and 68 in the ESCI. Unfortunately, since 2015, no Ukrainian journals have moved from ESCI to specialized indexes; moreover, several Ukrainian journals were excluded for publishing ethics violations. In 2019, the criteria of journal evaluation were updated/clarified. Today there are 28 criteria; 24 of them (quality criteria) are a prerequisite for inclusion into the ESCI. Journals applying to specialized indexes are evaluated according to four additional criteria of influence. The evaluation is carried out by the Clarivate Editorial Board consisting of company employees, who, in addition to professional skills, do not have any conflicts of interest. To initiate the journal evaluation process, the publisher fills out an online form and continues to publish the journal in a timely manner. Evaluation and subsequent indexing of the journal in the Web of Science Core Collection is a free procedure and the criteria are presented in the article.