What impact did the fall of the USSR really have on Western politics?

I'm taking an international relations class right now, so I can help a little bit to explain some changes in politics that should be just shy of the 20 year rule. The middle of the 20th century was essentially defined by the Cold War. This was a bipolar world and the very careful and strategic international policies were measured so as to exert as much influence as possible for each side without greatly angering the other. This can be seen with the more indirect policies in the so-called "third world." communist aid in Vietnam, US aid in Afghanistan, and varying attempts on both sides in Africa and Latin America. There was a great degree of tension on both sides that semi-ironically resulted in a fair amount of relative peace.

When the USSR disbanded, things changed somewhat rapidly. This was a collapse of the strongest power representing Communism that came from within. Various nonviolent revolutions resulted in breakaways of Soviet-aligned states such as Czechoslovakia, Hungary, and many others. In the capitalist world, this inspired a wave of general optimism that the liberal order truly would usher in prosperity across the globe. Probably the most prominent figure in this belief has been the political scientist Francis Fukuyama. Fukuyama formulated an end-of-history theory: That liberal capitalism and democracy will inherently become adopted across the world, and conflict and great hardship will generally fade away.

With these slightly more theoretical changes, there was also a massive shift in how the US chose to apply force internationally. The US had built up a military presence globally that was now essentially unrivalled. With this role as the sort of vanguard of liberalism, and the belief that less developed countries could be "helped" to get to that end of history state, the US started intervening in various conflicts across the globe, with varying amounts of success. Examples include the Gulf war, Somalia and Rwanda, and former Yugoslavia, though that last one might be getting too close to the 20 year rule.

I hope I did alright, as this is actually my first attempt at writing a comprehensive reply here. I will add sources in a few hours.

Fukuyama, Francis. The "End of History?". United States Institute of Peace, 1989.

Edit: Source

Edit^2: fact checking

Fukuyama, Francis. The "End of History?". United States Institute of Peace, 1989.