The Cold war confrontation between the US and USSR solidly redefined international politics after 1945. What divided their alliances during the war were their underlying ideological conflicts. Europe transformed into a major battle field; sharply divided. Such division characterized international relations and this made the world bipolar with both rigidity and a single world order ruled by confrontation of the superpowers as well as the mutual distrust.
This division was strengthened by military alliances. The US has created NATO that tied the western democracies. The Warsaw Pact was formed by the USSR that consolidated Eastern European satellites. This eastern and western block divided Europe into spheres, making the stalemate of geographical and military forces official and lasting decades.
The war was in proxy form world wide. This is because the super powers never confronted each other but provided one side with conflicts the world over. Korea, Vietnam, Afghanistan et al, were set up as battlegrounds. This policy exported the tensions of the cold war, killing local populations off with, at best, the deniability of the superpowers.
The introduction of the nuclear arms race brought in existential danger never before witnessed. The two powers amassed massive arsenals, and they attained Mutually Assured Destruction (MAD). This frightening balance stopped direct war without inhibiting espionage, crises such as Cuba, and the astronomical amounts of money spent in the world armies. International security consisted of the danger of destruction.
The competition of ideas saturated international institutions and decolonization. The USSR and the US took interest in dirtying their hands in the newly independent countries of Asia, Africa, and Latin America. The UN was one of the primary stages of their propaganda war and brought a global extension of the Cold War.
Conclusion:
The Cold War has had a fundamental change in the international system that has lasted more than forty years. It established a bipolar order, envisaged international military coalitions and proxy wars, and placed the nuclear deterrence at the center of security. That worldwide conflict of ideology and geopolitics predetermined the political orientations of the world and had a fundamental impact on the process of decolonization and regional conflicts. Its memory is still defining the international relations and security systems.