South Koreans could be extinct by 2750
Not only is the population aging (like in Japan and the US), but birth rates are falling and women are increasingly less inclined to get married.
In 2013, the country's birth rate plummeted to the lowest level on record: only 8.6 babies per 1,000 South Koreans were born, and the total number of births fell by 9.9% to the second lowest number on record.
Furthermore, a government survey of respondents aged 9 to 24 showed that only 45.6% of women "said marriage was something they should do in life," considerably lower than the 62.9% of men, according to the Brookings Institute.
Overall, the average South Korean woman is expected to give birth to 1.187 babies in her lifetime - the fifth lowest fertility in the world.
"A 2014 study commissioned by the national legislature concluded that South Koreans could 'face natural extinction by 2750 if the birthrate were maintained at 1.19 children per woman - assuming no reunification with North Korea or significant inflow of migrants," according to the Brookings Institute, citing data from a simulation commissioned by the National Assembly in Seoul.
According to that simulation, South Korea's current population of 50.2 million could fall to 20 million by the end of the century. The second largest city, Busan, will "go extinct" by 2413, while the capital, Seoul, will go by 2505.
(It is important to keep in mind that this is a demographic forecast 735 years into the future, so - to keep it simple - there is a lot of uncertainty in the projections and there will definitely be other variables that affect South Korea's demographics positively and negatively.)
However, there is another factor to consider: "mixed ethnic families" - where one parent is Korean (usually the father) and the other is not (usually the mother, from China, Vietnam or the Philippines).
Notably, the birth rate for children of immigrant mothers is higher than that of native Korean women. The number of school-age children from "mixed ethnic families" went up seven times from 2014 to 2006, and the number of adolescents from "mixed ethnic families" increased by 21% from 2013 to 2014.
As Katharine H.S. Moon writes for Brookings:
The face of the homogeneous South Korea we once knew is literally changing before our eyes as hundreds of thousands of foreign-born women marry Korean men and become Korean citizens and their multiracial/multi-ethnic children increase in numbers. An estimated third of all children born in 2020 (1.67 million) are expected to be of part Korean and part other Asian descent ("Kosian"), composing 3.3% of the total population. By 2020 and 2030 respectively, an estimated 5% and 10% of the South Korean population will be composed of foreign-born and immigrant families.
More immigrants would be good news for the Korean labor force, which is expected peak in 2016-2017. A report from December 2014 by the Korea Economic Research Institute even concluded that Korea needs as a many as 15 million immigrants (one-third of its population) by 2060 "to make up for a shrinking workforce and sustain growth."
And, as an interesting note from the culture angle, while from 2005-2010 80% of South Koreans believed that a Korean bloodline was essential to the "being Korean," that number fell to 65.8% by 2013.
The government is now even planning to make elementary school textbooks with "bi-ethnic/bi-racial children and multicultural families," according to Brookings.