The anonymous peer review is an unpublished pre-publication review which evaluates research articles submitted to journals. This type of a review plays a special role in the genre landscape of Anglophone research by ensuring its appropriate quality and ethical standards. By performing this role, the peer review also realizes a didactic potential, as it motivates researchers to improve their investigations. This paper extends the existing research on the anonymous peer review and aims to deepen our understanding of this genre by analysing the overall functional organization of peer review texts and their prominent linguistic features shaped by three communicative functions ‒ “gatekeeping”, evaluative, and didactic. It also attempts to compare the characteristics of peer reviews in two research fields ideologically and epistemologically distant from each other ‒ applied linguistics and applied mathematics. The methodological framework of the study combines Swales’s move analysis and a functional stylistic perspective developed within the East European linguistic context. The analysis has revealed a three-move structure of review texts and disclosed the roles of interpersonal markers, evaluative lexis and four types of directives in the realization of the communicative functions of the genre. The typologies of reviewers’ comments and evaluative acts in reviews have also been suggested. Furthermore, the study has brought to light some quantitative and qualitative differences between the texts in two disciplines. It is anticipated that awareness of the linguistic conventions of anonymous peer reviews analysed in the paper will help researchers to perceive this genre as a valuable source of professional assistance and enlightenment.