The Korean War. North and South Korea are still technically at war. An armistice was signed in 1953 to halt fighting, but no final treaty was signed, unlike after World War 2.
United States, NATO allies and South Korea fought against North Korea, who received aid from Chinese forces.
This an example of actual combat during the so-called Cold War between the United States and the Soviet Union between 1945-1991. The two sides had different ideologies (democracy vs. communism), which led to friction.
