The political status of Taiwan is controversial. Not only is it controversial whether Taiwan should remain as part of the Republic of China, become part of the People's Republic of China, or become an independent Republic of Taiwan, different groups have different concepts of what the current situation is.
The political solution that is acceptable to most of the current groups is the status quo, which is to leave Taiwan's status the way that it is.
The current position of the People's Republic of China is that Taiwan is part of China and the PRC is the sole legitimate government of China. In addition to the problem the People's Republic of China is unwilling to negotiate under any other formulation than a one China policy.
Within Taiwan, support for Taiwan independence and Chinese reunification exists as part of a political spectrum with most people apparently in the middle.
The current controversy is over the term one China, which the PRC insists is necessary to begin negotiations.
-> When given a choice between the three options of independence, status quo, or unification, typical results of recent polls show 20% in favor of independence, 15% in favor of unification, and about 50% in favor of status quo.