While Taiwan was ruled by Chiang Kai-shek's Kuomintang (KMT) party, independence was not really an issue because the KMT's aim was to take back control of all China. But in the 1980s, as Taiwan introduced democracy, the opposition Democratic Progressive Party (DPP) came to prominence, with a clearly-stated goal of independence for the island.
This stance seriously alarmed China, which saw its "one China" policy under threat. Beijing repeatedly warned that any declaration of independence by Taiwan would be a justification for war.
The DPP goal was put on hold when its candidate, Chen Shui-bian, won the 2000 presidential election. Perhaps hoping for a breakthrough with Beijing, he immediately announced that, so long as China did not use force, he would not declare independence.
But China refused to deal with President Chen, who responded by calling for - and getting passed - a referendum law. He promised not to use the law to poll people on the island's status. But its passage infuriated Beijing, who saw it as another move towards independence, and also as a further complication for persuading Taiwan to reunify.
Officially, the DPP still favours eventual independence for Taiwan, while the KMT favours eventual re-unification. Since neither outcome looks likely in the short or even medium term, it is perhaps not surprising that opinion polls suggest most Taiwanese people want things to stay as they are, with the island's ambiguous status unresolved.
Set against that, more and more people say they feel Taiwanese, rather than Chinese, suggesting the independence debate will only get fiercer.