1968: North Koreans captured USS Pueblo.
Excerpt from History.com:
On January 23, 1968, the USS Pueblo, a Navy intelligence vessel, is engaged in a routine surveillance of the North Korean coast when it is intercepted by North Korean patrol boats. According to U.S. reports, the Pueblo was in international waters almost 16 miles from shore, but the North Koreans turned their guns on the lightly armed vessel and demanded its surrender. The Americans attempted to escape, and the North Koreans opened fire, wounding the commander and two others. With capture inevitable, the Americans stalled for time, destroying the classified information aboard while taking further fire. Several more crew members were wounded.
Finally, the Pueblo was boarded and taken to Wonson. There, the 83-man crew was bound and blindfolded and transported to Pyongyang, where they were charged with spying within North Korea's 12-mile territorial limit and imprisoned. It was the biggest crisis in two years of increased tension and minor skirmishes between the United States and North Korea.
The United States maintained that the Pueblo had been in international waters and demanded the release of the captive sailors. With the Tet Offensive raging 2,000 miles to the south in Vietnam, President Lyndon Johnson ordered no direct retaliation, but the United States began a military buildup in the area. North Korean authorities, meanwhile, coerced a confession and apology out of Pueblo commander Bucher, in which he stated, "I will never again be a party to any disgraceful act of aggression of this type." The rest of the crew also signed a confession under threat of torture.
The prisoners were then taken to a second compound in the countryside near Pyongyang, where they were forced to study propaganda materials and beaten for straying from the compound's strict rules. In August, the North Koreans staged a phony news conference in which the prisoners were to praise their humane treatment, but the Americans thwarted the Koreans by inserting innuendoes and sarcastic language into their statements. Some prisoners also rebelled in photo shoots by casually sticking out their middle finger; a gesture that their captors didn't understand. Later, the North Koreans caught on and beat the Americans for a week.
On December 23, 1968, exactly 11 months after the Pueblo's capture, U.S. and North Korean negotiators reached a settlement to resolve the crisis. Under the settlement's terms, the United States admitted the ship's intrusion into North Korean territory, apologized for the action, and pledged to cease any future such action. That day, the surviving 82 crewmen walked one by one across the "Bridge of No Return" at Panmunjon to freedom in South Korea. They were hailed as heroes and returned home to the United States in time for Christmas.
Incidents between North Korea and the United States continued in 1969, and in April 1969 a North Korean MiG fighter shot down a U.S. Navy intelligence aircraft, killing all 31 men aboard. In 1970, quiet returned to the demilitarized zone.