The article on the Convention on the Prevention and Punishment of the Crime of Genocide (hereinafter Genocide Convention) aims to cover fundamental principles of the Genocide Convention and problematic issues concerning its application. The methodological section on the international relations theory is followed by a description of sociolegal and historical context at the time of adoption of the Genocide Convention. The second part focuses on the content of the Convention; the third part analyzes the first situation defined as an act of genocide, the Rwanda genocide. The emphasis is given to the Akayesu Case and judicial activism in relation to the protected groups within the genocide definition. The last part concerns the possibilities of the further development of the prohibition of genocide.