By the 1860's most of the world had been opened to trade, either via diplomacy or force, to trade with the developed western nations. However, numerous countries in east Asia continued to resist by setting up strict isolationist policies. The leaders of these countries had watched India and southeast Asia get swallowed up by the great western colonial empires and so understandably had little interest in so-called offers of friendship. Into this world blundered the United States. Fresh off of a successful opening of trade relations with Japan in 1855, by which I mean US naval ships just kind of showed up with a bunch of guns and their proverbial dicks wagging all about, the American government was pretty sure it could do it again in the little understood nation of Korea.
Korea at the time was ruled by an emperor of the Joseon dynasty, a group that had ruled the peninsula for over 450 years. Having watched the strong-arming of the Chinese and Japanese over the preceding decades, the Joseon were less than cool with the idea of opening themselves up to such shenanigans. If they found a shipwrecked sailor they would gladly return them, but overall a policy of 'don't say a damn thing to those foreign dogs' was the norm.
This was less than acceptable to American traders, many of whom supposed that Korea must have some pretty cool shit hiding away. Tiring of such shit, in 1866 a group of these traders boarded an armed merchantman named the General Sherman to force the issue. The General Sherman arrived at Korea uninvited and anchored near one of its largest cities. The Koreans, less than happy with this ordered them to leave, to which the traders responded by taking hostages and firing cannonballs randomly into the city. What followed was a four day battle which ended with the General Sherman blown the fuck up and all of its crew killed.
Fast forward five years to 1871 and the US was ready to try it again. However, this time instead of a random group of merchant they sent five US navy warships and some 650 sailors and marines. The timing was probably not all that great. The whole General Sherman thing had been followed a few months later by an attack by the French navy over the murder of a couple of Catholic missionaries who had been in Korea illegally. So sufficed to say, the Koreans had really doubled down on the whole isolationism thing. When the US naval expedition arrived they landed a small group at the mouth of the Han River, which led directly to Korea's capital of Seoul. There they met with local officials who were told that the Americans planned to sail up the river, which was unfortunately mistranslated as we'll just be on our way, because when it comes to misunderstandings history works exactly the same as romantic comedies. When the US warships started sailing up the river the Koreans freaked the hell out and started firing cannons at them from numerous forts on the shoreline. Put off by the whole thing, the Americans retreated and then sent a demand that the Koreans apologize for the incident within ten days. The Koreans, feeling like they were owed an apology, refused.
After the ten days had passed the US landed their marines which started attacking one fort after another. The Korean defenders, being from an isolated country and all, were only armed with matchlock muskets and old school cannons, while the marines were armed with repeating rifles and modern artillery. It goes without saying that things did not go well for the Koreans. In just fifteen minutes the US marines destroyed five forts and killed 243 Korean soldiers, all while only losing three soldiers of their own. However, despite the victory, the Koreans weren't beaten. The Americans lacked the firepower to go further up the river and the Koreans absolutely refused to negotiate. When the Americans offered to return prisoners they had taken in hopes of opening up talks, the Koreans told them it was okay if they executed them since they were all cowards. Unable to do a damn thing, the US expedition hung around for about twenty days before dejectedly sailing for home.
Though Korea won the day, the ease by which the US beat the shit out of them made it apparent to its rulers that they couldn't stay isolationist forever. In 1876 they opened trade with Japan, the US in 1882, and the British in 1885. However, over time Korea increasingly fell under Japan's power, eventually being fully annexed by its more powerful neighbor in 1910.