The article is devoted to the institution of review of court`s decisions on newly discovered or exceptional circumstances, which is considered as a mechanism to ensure the right of everyone to a fair trial. The key features of the institution of review of court decisions on newly discovered or exceptional circumstances, which distinguishes such review from the review by courts of higher instances are considered, such as aim, object and subjects of review. In particular, it was determined that the object of review may be court decisions that have entered into force and which have completed the proceedings; the subject of review is the court of the instance that made the decision, for review of which the applicant requests; the grounds for review may be only the grounds defined by law as newly discovered or exceptional circumstances, and decisions are reviewed not on the subject of judicial error, but in connection with the identification of the outlined circumstances. The general characteristic of the procedure of review of court decisions on newly discovered or exceptional circumstances in the civil process of Ukraine is given.