In the 1500's, Christian missionaries came to Japan and started gaining converts. But in the 1600's, the new religion was violently suppressed, and Christianity only survived underground among the Kakure Kirishitans (Hidden Christians) until the 19th century. When the Shogunate ended and the country reformed, Christianity was permitted again, but to this day it is a very small minority religion in a country dominated by Buddhism and Shinto.
How and why?
In the 1500's, Japan was in turmoil, with various feudal warlords battling it out with each other. In the midst of this, the Franciscans, Dominicans, and Jesuits had ample opportunity to gain converts. They continued to gain ground until the entire situation changed. At the end of the 1500s, the three great unifiers -- Nobunaga, Hideyoshi, and Tokugawa Ieyasu -- campaigned to unite the country under their rule. This culminated in Ieyasu's victory at the Battle of Sekigahara (1600), after which Japan was ruled by the Tokugawa Shogunate. In the process of this, they had overcome many challenges, including Buddhist monasteries which often held significant land, wealth, and power. Once in power, the Tokugawa Shogunate was determined to maintain their authority, keep the country united, and enforce a feudal hierarchy throughout their domain. To this end, they restricted foreign trade and immigration/emigration through Sakoku, and instituted various measures for unification, such as the Sankin Kotai.
And so, you had a government that understood the dangers of an independent religious faction (because of their experience with the Buddhists), and one that distrusted foreign influence as a destabilizing factor in their project to unify and administer Japan. To make matters worse, the Shogunate understood that Christian doctrine placed God and Jesus above all secular authority, and that Catholicism in particular was loyal to the Pope in Rome -- seemingly a challenge to their rule. In addition to this, if a Daimyo embraced Christianity, he could force this belief on his population, as Omura Sumitada in fact did in the late 1500's. The shogunate of course perceived this as a threat. While there had been conflict with Buddhism, it had a very long history as a native tradition. This was not the case with Christianity, plus it was espoused by foreign European powers.
Buddhism was co-opted by the Shogunate, while Christianity was persecuted and made illegal. Mass expulsions and executions followed. If the Shogunate had any reservations about the proscription of Christianity, these were ended by the Shimabara rebellion. This uprising was triggered by excessive taxes and by Christian persecution, and many of the leaders and followers of the rebellion were Christian. Not only did they defy the Shogunate, but they attacked native traditions, including an incident in which the rebels beheaded Buddhist statues of the Jizo Bodhisattva. The rebellion was put down, and needless to say, their actions did not go over too well. Sakoku (national seclusion) was tightened, and Christian persecution was intensified. The Tokugawa shogunate utilized torture and execution to suppress Christianity -- if Christians did not recant their faith under duress, they were killed. Having co-opted Buddhism, they made it compulsory for Japanese to register at a local Buddhist temple, which assisted in Christian persecution (as well as provided valuable census information and a means of surveillance and control). To identify Christians, Japanese were forced to stamp down and tread their foot on a metallic engraved image of Jesus on the Cross or Mary (fumi-e). Anyone who refused to do this was identified as a Christian. They also used propaganda and other means to ensure that Christianity would not be tolerated.
Even after all this, the religion was not extirpated. Small communities continued to practice Christianity and hold Mass, known as Kakure Kirishitans (Hidden Christians). But they existed underground, always hiding from a Shogunate that would torture them into apostasy or kill them. They used many methods to practice their faith in secret, such as disguising their Christian relics as Buddhist.
As I mentioned in the lede, persecution of Christianity ended with the Shogunate. Christianity and even evangelism is legal and permissible in Japan today. However, this history left its mark, as only ~1% of Japan's population professes Christianity. Japanese culture is wedded to Buddhism and Shinto, and missionaries have made little headway.