Like every country, China has peculiarities in how it is run. One of these is how the General Secretary of the Communist Party of China is the leader of the country instead of the president, prime minister, chancellor, or any other such position (though traditionally the general secretary also assumes the mostly ceremonial position of president as well).
The current iteration of the post came in 1982, when Hu Yaobang took the post, initiating reforms. He was dethroned in 1987 for not ceding to the demands of Deng Xiaoping (the then still de facto ruler of China) to deal with the leaders of student protests for more liberties. The Tiananmen Square protests of 1989 were preceded by Hu’s death and the wish of students to honour him.
Hu was succeeded by Zhao Ziyang, who took up and continued many of Hu’s reforms. He resigned when Deng Xiaoping ordered troops to deal with the Tiananmen Square protests.
Jiang Zemin took up the mantle for the remaining and two more terms. With the death of Deng Xiaoping and the waning influence of the eight elders, Jiang was able to turn his de jure leadership of China into a de facto one. He introduced another set of reforms, centralising a lot of the political power and relaxing many economic restrictions. He resigned in 2002, making room for Hu Jintao.
Hu Jintao aimed to balance out the inequalities that had arisen over the previous decades by adding regulations for the economy and protecting the environment. He stepped down after his two terms were up.
His successor and and current office holder is Xi Jinping.
With the exception of Jiang Zemin, who had to step up after his predecessor was factually ousted from his position, all general secretaries stepped down from their office when their second term was up. Even Jiang did after his second ‘regular’ term.
But there’s doubt Xi will do so as well. Usually a successor was introduced into the Politburo with the second term (young enough to serve two 5-year terms themselves), but Xi notably did not do that in 2017. Some see this, as well as his chairing many leadership positions and changing the constitution to abolish term limits for the presidency, as signs Xi aims for a third term in 2022.
Will Xi Jinping keep leading China past 2022?
This question will resolve as Yes if:
Xi begins serving a third consecutive term as General Secretary of the Communist Party of China, or
Xi remains paramount leader past 2022, or
Xi remains de facto leader of China if either of these positions loose their importance in Chinese politics.