The flag of South Korea is called the Taegeukgi. Its design is drawn almost entirely from East Asian philosophy rather than from heraldry or party colors, which makes it unusual among national flags.
From Gojong to the Republic
The flag was first adopted in 1883, under the Joseon Dynasty, during a period of attempts to modernize the state and give it a national identity legible to the outside world.
Japan restricted its use during the occupation of 1910 to 1945, as part of a broader effort to suppress Korean culture. Being banned did the flag no harm. After the war and the division of the peninsula, the Republic of Korea, founded in 1948, standardized the design on October 15, 1949.
Later changes have been small: adjustments to proportions and to the shapes of the symbols, to bring the flag into line with government standards. Most of that tidying happened after the Korean War, as the country rebuilt.
The taegeuk and the four gwae
The field is white, associated in Confucian thought with purity and integrity. At the center is the taegeuk, a circle split into a red and a blue swirl. It comes from yin-yang philosophy, and the point of it is interdependence: neither half makes sense without the other.
Four black trigrams, the gwae, sit at the corners, arranged so that each faces its opposite across the taegeuk. Upper hoist is geon, heaven, standing for justice and virtue, with gon, earth, for receptivity and devotion, diagonally opposite at the lower fly. Upper fly is gam, water, for adaptability, with ri, fire, for clarity and radiance, at the lower hoist. The trigrams come from Chinese cosmology and Korean Confucianism, and each one names a basic element of the order of things.
The flag takes its name from that central symbol.
Flying it
The Taegeukgi is flown on government buildings and on national holidays including Liberation Day and Korean Independence Day. The rules covering its display are strict, down to how it should be folded.
Naval and military variants add service emblems to the basic design. Abroad, the flag appears at diplomatic posts and at international competitions.
In Korean life
The flag is taught in schools, and it turns up steadily in film, television, and writing, usually as shorthand for endurance. At international sporting events it is the rallying point for South Koreans and for the diaspora.
References
[1] Korean Government Official Website: Korea.net [https://www.korea.net/]
[2] Korean Vexillological Association Resources
[3] "History of the Korean Flag" - Ministry of Patriots and Veterans Affairs, South Korea
[4] UNESCO World Heritage Documents: Korean Cultural Traditions
[5] "Korean History and Culture Textbook" - Lee, Peter H., 2012