The very first summit of the most industrialized states was held in Rambouillet in 1975. However, the name G7 became official in 1976, when Canadian participants joined the representatives of France, Germany, Great Britain, Italy, Japan and the US. The transformation into G8 was formally made possible in 1998, during the Birmingham summit. Economic declarations and summit communiqués are the most important documents to come out of the summits. They include recommendations for members of the group and they also contain proposals directed to the regions or the particular states. Even though it is economic matters which are the major leaders' main interests during the summits, the political dimension of the meetings, especially in terms of its global aspects, is also very important to the international environment. The key objective of this article is to present the attitude of the G7/G8 towards the following problems: transnational crime, especially that in connection with illicit drugs and bribery, international terrorism, nuclear safety, arms control, the proliferation of weapons of mass destruction and UN reforms. The areas of the science, social and cultural cooperation have also been included. The paper attempts to sum up the involvement of the G7/G8 in all these issues during the period of more than 30 years in which it has been active. Importance has been placed on introducing the most decisive initiatives and common projects, linked with the process of both building the new institutional bodies and releasing treaties, conventions and acts. The effectiveness of particular initiatives is a more complex matter and requires further research.