This article analyzes contemporary issues arising in the adjudication of criminal cases involving the crime of aggression before the International Criminal Court (hereinafter, the ICC). The analysis includes the relevant provisions of international law governing the organization and functioning of international criminal justice institutions, as well as the practice of their application. The article examines the stages in the emergence and development of international criminal justice, the activities of the ICC in investigating crimes within its jurisdiction (primarily the crime of aggression), and various approaches to defining the international crime of aggression. The authors identify and systematize the principal challenges that impede the effective functioning of the ICC in the investigation of international crimes. They also propose and substantiate a set of measures aimed at addressing these challenges.