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troperville

The Republic of Korea Armed Forces was founded in 1948 in response to North Korean attacks leading to the Korean War. Most of the army at that time was more like a gendarmerie than a full army; when the North rolled its troops across the South, they curbstomped South Korea, until the United States decided to step in (and for a while afterward); the ROKAF later Took a Level in Badass, but a Chinese ~~mercenary~~ voluntary army was sent by Mao Zedong, partly to help Kim Il-sung and partly because Mao feared China would be attacked by the U.S. via Manchuria; a grinding war ensued until 1953, ending with Korea still being divided into two.

When South Korea's economy grew in the 1960s and 1970s, then-President Park Chung-hee encouraged military industry, first by making licensed copies of American military equipment, and later indigenous designs. Due to the North Korean threat, the Republic of Korea Armed Forces have a large budget.

South Korea is a key ally of the United States; it is said that losing South Korea (to North Korea or China) will be disastrous for Asia, and Japan is having doubts about America's ability to protect the region and is considering wheter it should make its own Kaiju Defense Force as badass as shown in anime. Japan's concerns have been curbed somewhat by a new American foreign policy emphasizing focus on East Asia and the Pacific.

The Republic of Korea Navy is building a light aircraft carrier and plans to be a blue-water navy by 2020...if the North doesn't invade before then.

The South Korean Armed Forces is modeled after the way the US military worked between the National Security Act of 1947

and the Goldwater-Nichols Act

of 1986; this means that while the chain of command runs from the President through the Minister of National Defense, advised by career military Joint Chiefs of Staff, the Joint Chiefs are also in the operational chain of command of their respective branches, rather than serving as advisors with command running directly from the civilian officials to combatant commands. This difference is rendered irrelevant by the nature of South Korea's defense needs: the US has a combatant command for each theater of operations plus one each for special forces, nuclear weapons, and logistics. However, South Korea only has one theater of operations to speak of, has no nukes, and its special forces and logistics needs don't require a top-level command, so the Chairman of the Joint Chiefs is basically the commander for the country's lone combatant command. Also borrowed from the Yanks With Tanks is the presence of a quasi-independent Marine Corps theoretically subordinate to the Navy but really an elite combined-arms fourth branch of the military.

Conscription is mandatory for males 18 and above for at least two years. It is regarded as a Serious Business for South Koreans, actors and entertainers included, to perform the service, and trying to avoid service is a serious offense and can cause any person to be imprisoned for a time.

Despite the title, has nothing to do with South Korea's use of other Marines.

Republic of Korea Army

The Republic of Korea Army is the senior branch of the armed forces. Its size of 600,000 is understandable because any North Korean Zerg Rush to the south is complete trouble. South Korean Army troops are known to be a Badass Army; in Vietnam, both the Americans and Vietnamese from both sides respected the ROKA because their tactics seemed to work better than those of either of the U.S. or the South Vietnamese.

South Korea has mandatory military conscription - every Korean male, with very few exceptions, serves about 2 years in the military after graduation.

The ROKA currently fields the K1 tank, which is as good as the M1 Abrams tank according to its creators, and the K200 and K21 series armored personnel carriers. Bizarrely enough, they also have 35 T-80 tanks that were given as part of a payment of debts the Russians owed them.

Republic of Korea Navy

The Republic of Korea Navy is the naval branch of the ROK armed forces. Many ROK navy men revere Admiral Yi Sun Shin, who in the 16th century whacked a Japanese invasion fleet with his Turtle Boats, the world's first ironclads (no, really). The South Korean navy is currently building up its forces, including an amphibious assault ship/light carrier, to make it a blue-water navy in 2020 like that of its eastern neighbor and rival.

Republic of Korea Air Force

The ROK Air Force is the air arm of the Korean armed forces. It has 600 American-designed planes, most of them F-4 Phantom IIs, F-5 Tiger IIs, and F-16 Fighting Falcons, but it is currently including the F-15E Strike Eagle and the T-50 Golden Eagle (unrelated to the former) trainer/attack fighter. The ROK Air Force wants to have JDAM bombs and attack drones so that their aircraft have better Macross Missile Massacre ability.

Currently, they are designing their answer to the F-22, though it seems to be in Development Hell.

Republic of Korea Marines

The Trope Namer, the ROKMAR, although theoretically under the direction of the Chief of Naval Operations, operates as a distinct arm of the military of South Korea. It has a Badass reputation; during the Korean and Vietnam Wars, they were so successful in fishing out North Korean and Vietcong guerrillas that they earned the nickname "Ghost-Catching Marines." One example in Korea is that a squad of ROK Marines had almost decimated an entire North Korean battalion. In Vietnam, the Vietcong and the NVA dreaded fighting Korean Marines; one battle involved 300 South Koreans successfully fending off an entire North Vietnamese brigade with minimal casualties. They were famous for their special style of combat, and ROK commandos sometimes killed Vietcong with karate chops in close-up fights. By comparison, American soldiers in Vietnam had a lower kill ratio than the Koreans, serving only to further their reputation as badasses around the world.

KATUSA: Korean Augmentation To the United States Army

Eagle Squadron, except that they serve with US Forces in South Korea. Young Korean men have to pass English proficiency tests then are selected by lottery for training. After training, they serve with US units in Korea. Many families would like to see their sons enter the KATUSA program because of the ROK Army and Marines training from hell/Spartan Way. KATUSA soldiers do enjoy their time with US units. However if they fail a PT test or violate US and ROK military regulations they get sent back to a ROK Army unit.

Examples in fiction:

The South Korean Army appears in Mercenaries as one of the factions invading North Korea. They are depicted as being supported by the American CIA, and are equipped at the same level as the Allied Nations expedition.
Also features prominently in the Korean War film Taegukgi.
The Dale Brown novel Battle Born, involving a Second Korean War.
Play a large role in the Larry Bond novel Red Phoenix, where an ROK liaison officer is one of the two survivors of one of the opening attacks in a Second Korean War.
An episode of The Unit is set on a South Korean submarine.
Every so often, ROK military personnel show up in, well, M*A*S*H.
ROK forces are a thorn in your side in the Soviet Campaign of Command & Conquer Red Alert 2, conducting a raid on the Russian Far East and screwing up your invasion of Hawaii. They also get quite possibly the most awesome special unit on the Allied side in multiplayer/skirmish mode: the Black Eagle, a better version of the usual Allied Harrier fighter plane.
Korean soldiers are the main characters in two Korean horror movies directed by Kong Su-Chang. R-Point, set in Vietnam during the Vietnam War and The Guard Post, set on the DMZ in modern day Korea. The Other Wiki has detailed synopses of both.
South Korean soldiers appear in the Seoul mission in Splinter Cell: Chaos Theory. Notably, they are just as hostile to Sam as North Korean soldiers are, if only because a guy in a full black suit with guns and tools strapped all over sneaking around an active warzone would look pretty suspicious to anyone.