I can answer the second part of your question in regards to Japan.
Christianity came to Japan in 1543 when a Portuguese trade ship showed up on a small island just off it's shores. Missionaries came to Japan, specifically the Jesuits. They learned Japanese and began building churches. About a quarter million Japanese people were converted in this time, including some warlords. The reasons for a warlord to convert where wide. Some did it for better trade, some did it for guns and cannons, and some for genuine belief. In fact, one of the most powerful warlords were was quite enthused with Christianity: Oda Nobunaga. Nobunaga was the most powerful warlord in central Japan by 1580. In fact, Nobunaga was more lenient with Christians than he was with many Buddhists.
However, upon Nobunaga's death, his second in command took charge of his holdings. This man was Toyotomi Hideyoshi. Hideyoshi was less tolerant of Christians and began suppressing Christian activities. After Hideyoshi's death, the Tokugawa family came to power in Japan and the Tokugawa really didn't like Christians. They weren't too fond of Europeans in general and kept Europeans off of Japanese soil as much as they could while still trading with them. Christianity was outlawed and driven underground.
I can answer this one to the best of my abilities (I have a bachelors degree in history with a focus in Asian history)
This all begins from the benefits of the Choson Korean government paying 'tribute' to Ming China. When the government sent merchants along with officials to trade resources and obtain literature from around the world (such as the bible). This tribute system continued up until the Ming were essentially out of power. Now when European powers began to trade with the major Asian powers (Choson Korea, Ming China, Tokguawa Japan) each country had their ways of dealing with this new influx of trade that began to shift in the benefit of the European powers (Japan rapidly changed altogether from the Commodore Perry trip and when they saw the ming begin to crumble, China falls apart) Some Koreans began to view western thinking as being progressive! Such western thinking such as the Bible.
The Korean leader saw how China fell apart and Japan's current government taken away so in order to sustain his power he cancelled all trade with European powers. Because you need to be literate to read the bible, many Korean Christians were intelligent and played a key part (writing in the newspaper, organizing ect.) in taking down the regime. When Japan took over this group of people continued to be active.
This group alone didn't take down these governments as they received great help from other Koreans that weren't Christians but Korea is one (if not the one) of the countries to have a heavy Christian presence without much missionary work done to in the country and the reason why is because it was seen as being progressive.
TL;DR: Some Koreans saw Christianity as a way of improving themselves/Korean Society.
According to "A History of Korea" by Michael J. Seth, Korea really began finding converts to Christianity during the Choson dynasty in the 17th-18th centuries as part of a wave of Western influence (that included things like potatoes and hot peppers). Some Koreans, captured during the Japanese invasions, were converted in Japan. One notable convert was baptized as "Antonio Corea", ended up in Italy in 1606, married and set up a life there, never returning to his home country.
Korea during this time was also heavily isolationist and didn't allow foreigners (including missionaries) into the kingdom. This is the time period where the term "Hermit Kingdom" originated. However, Korea, as a tributary of China, did send frequent embassies to Beijing, which included various trade activities as well as cultural exchanges. A Jesuit mission in Beijing, established by Matteo Ricci (1552-1610), greatly impressed the Chinese imperial court with their painting skills, telescopes, grape wine, geography, map making, mathematics, accurate calendars and other Western bits of technology and knowledge and were often employed by the Imperial court to perform some of these services. Korean embassies were introduced to these foreigners and their wild ideas through these exchanges. The Jesuits even provided Koreans with their first sky calendar allowing them to calculate the position of the heavens over Seoul...instead of Beijing, allowing them to more accurate plan crop planting and other agricultural management needs.
Koreans were also impressed with the technological sophistication, but considered Western culture barbaric and unimpressive, which included Western religions. However, a few noblemen did get converted while visiting Beijing during embassy tours. During the late 18th century, most of these early converts were politically disenfranchised people from the aristocratic caste who belonged to an out-of-power political faction (the Namin). Most of these converts would have been considered intellectuals or scholars in Korea, which is unusual as Christianity typically spread by converting low class groups.
More unusual, many of these intellectuals brought back Chinese translations of Christian literature and found the ideas appealing. While back in Korea, they essentially converted themselves, even staging baptisms and other ceremonies.
In 1742, the Pope ruled that ancestor worship (central to Confucian practice) and Catholicism were incompatible. This begun a general purge of Catholic missions in China as well as converts in Korea. In 1795 a Chinese Priest, Zhou Wenmo, was asked to come to Korea by the small underground Christian community and started rapidly converting people. Some political protection was provided when a converted aristocrat from the Namin faction found himself in a significantly influential position during the reign of King Chongjo.
In the early 19th century, Christian Koreans even started sending out appeals to the Catholic church to send military forces to force the purges to stop. These letters were often discovered and only increased the intensity of the purges, but by this time there were thousands of Christians in Korea. Mass executions of high-level Christians became a frequent tactic to put down the Christian groups.
A change in power in the Korean leadership put off the purges while they secured power, and this window provided an opportunity for the Vatican to send 3 French priests (Maubant, Chastan and Imbert) to secretly enter the country. The first Korean priest (Kim Tae-gon) was ordained in Macau and then also smuggled into the country. There were around 9,000 Christians at this time.
During the 19th century, Western imperial powers poked around near Korea, but never found it interesting enough to really invade or force open so missionaries could start conversions. However, in 1839, the three French priests were executed as part of a new purge, which caused France to send warships to Korea. The government, furious at these foreigners, Father Kim Tae-gon was executed and purges continued.
Again another change in government in 1849 caused the purges to stop, and again the Vatican sent more priests, this time 12. By 1864 there were 20,000 converts. Most of these converts followed the typical conversion pattern, urban poor and outcast, the destitute, etc.
By now Christians were small but growing minority. In 1866 a massive purge started and thousands of converts were killed as well as many of the French priests. Again the French sent ships to check this out, except this time they started several minor skirmishes and captured a tiny bit of territory before being driven out.
In addition, another foreign ship, and American ship the General Sherman tried to force open Korea, but the ship was captured and the crew killed. The U.S. sent three expeditions to investigate, finally sending 3 ships and 1,200 men to seize territory and had some success before being repelled.
Simultaneously to all this, a syncretic religion appeared called Tonghak that blended traditional Confucian and Shamanistic beliefs with Christianity and spread quickly. This group caused numerous peasant revolts. It later turned into the Cheondoism movement (and the factional Suwunism). But you can imagine that converting from Christianity to Cheondoism is a slightly easier process than other previous paths.
During the Japanese colonial period, American Presbyterian missionaries (lead by Horace Allen and Horace Underwood) entered, starting in 1880. American cultural dominance was often cited as a reason for conversion and early converts included Syngman Rhee.
The Japanese colonial government, seeing Christianity as a rebellious group with links to the assassination of governor-general Ito Hirobumi, also started purges in the early 1900s. From about that point on, Christianity and Korean national identity (and resistance to Japanese occupation) started to converge. Hundreds of churches were destroyed and hundreds to thousands of people killed and possibly tens of thousands arrested. All this gelled into a counter-Japanese movement called the "March First Movement". These nationalists started taking leadership roles in various moderate and radical nationalist movements and became so prominent that when the Japanese finally left Korea, the immediate attempt by Koreans and building a government built a small council in Pyongyang that was mostly made up of Presbyterians. Kim Il Sung, first leader of North Korea, was even raised in a protestant household (he's regarded as also co-opting significant portions of Christian symbolism as part of his cult of personality).
Koreans during this time period also criticizes their national weakness that lead up to the Japanese occupation by their rejection of Western ideas in favor of "inferior" Chinese ones, this included Christianity. Korean women's rights groups were also composed of largely Christian Koreans (as older Confucian models and the Choson social structure was strongly repressive of women). This culminated with the establishment of the prestigious Ewha Women's College in Seoul.
Later during the South Korean military dictatorships, Christian groups once again found themselves as part of dissident groups. They were often responsible for organizing labor, ran human rights campaigns and other anti-government activities. Christianity also played an important role in de-castification in post-colonial times. The Seoul Cathedral was often a site of refuge for protesters fighting against the dictatorial government in Korea. A Presbyterian Christian Academy also found similar uses as an anti-government safe-zone. The government, not eager to invite foreign intervention, usually decided to leave the Churches alone.
Basically South Korean politics have become dominated by politically active Christian groups and it's become popular to become "Christian" in order to politically engage or actively participate in labor unions. Several political ideologies rooted in Christian philosophy and concepts of social justice have also sprung up, like minjung, a radical popularism. Belonging to foreign Churches and Church sponsored groups like labor unions also offered a degree of protection from political prosecution and offered economic security.
Estimates on the number of actual Christians vary, but are often wildly optimistic. It's guessed that about 1/3 of the population self-identify as Christian today, or under 17 million. However, this includes very nominal Christians as well as members of the very large number of Christian affiliated religious cults like the Unification Church (the "Moonies") or the Evangelical Baptist Church of Korea (owners of the Sewol Ferry) -- there are literally thousands of small "Christian" cults in Korea and parsing them from mainstream Christianity can be pretty hard.
MOD NOTE: This question is about the popularity of Christianity in South Korea. Dropping in to note that the Philippines are majority Christian or that various other Asian countries have (single digit percentages of) Christian populations is not answering the question. Please respect the OP by trying to answer their question, not giving demographic trivia.
edit: Per OP, other countries' Christian histories are OK. Comments must still meet /r/AskHistorians standards, which "Country X actually has Y% Christians," does not.
As Japanese,I know roughly why christianity is not popular in Japan. What Christianity explain how world and space,nature,life,human formed is not match what we feel at daily life.
In Japan,Two major religions Shinto and Buddhism believed here. Most Japanese believe this two religions at same time.
Shinto well express how Japanese feel nature and life. Shinto explain god exist in everywhere ,even stone. Shinto's view of the world is very flat. On the other hand,Christianity explain that one god only exists and god exists at world of center or top. This view of world is not Japanese taste and sense.
Buddhism is good at explaining life and nature(ex.cycle of reincarnation) theoretically. Shinto = feel,sense of world and nature,life Buddhism = theory of how world and nature,life formed. These two religion give Japanese sense of understanding the world and life.
Additionally, Christianity is gloomy,depressing image from Japanese view. at big station like Shinjuku ,Akihabara,some pale faced Japanese christian preaching with speaker is usual scene. People look at them instinctively think that this religion is not good. I think it looks better to send a bunch of gospel singer here.
#sorry for my engrish.thx!!