Statistics document a steady rise in terrorism during the 1970's and considerable growth in explosive bombings, incendiary attacks, and assassination attempts. The paper argues that terrorism is a serious world problem because it threatens innocent life and rights and directly attacks the national legal systems. Current trends are surveyed, including Soviet training for guerillas, the growth of proterrorist subcultures in developed states' universities and cultural centers, increased cooperation among terrorist organizations, and terrorists' acquisition of increasingly sophisticated weaponry. Also discussed are targets, transnational attacks, and assassin sects. The paper explores the effectiveness of United Nations conventions and committees, international cooperation among police and intelligence agencies, bilateral agreements, and extradition problems. Suggestions to improve state and international response to terrorism address internal political and economic stability, avoiding overreaction, international cooperation, and countering propaganda. 26 footnotes.