This chapter discusses the strategy that the EU intends pursuing in 2020–2025 with regard to the containment of serious transnational crime in order to show the necessity for international cooperation. It briefly discusses the machinery that has been constructed in recent decades to combat certain major cross-border forms of serious crime in a targeted and effective manner. That machinery forms the infrastructure required to implement the strategy against serious transnational crime in the strict sense. The chapter addresses, as far as possible, the problem at which the strategy is aimed. The gravity of the problem of serious transnational crime cannot be quantified solely based on sources which claim to contain direct data on the reality of this problem and to thus represent it as effectively as possible.