The major problem between Taiwan and China is the Taiwanese economy. If the island state had never managed to industrialize under the GMD, it would have been absorbed by the CCP and the rest of mainland China long ago. As is, its strong economy, international trade and connections keep it steadily propped up in its uneven fight. Globalization and fine balance between defence and parlay of Taiwan are the only things that will keep it out of the hands of China.
Taiwan’s modern life began the start of the peoples republic of China; almost all of the fleeing neo-fascist and capitalist Goumindang went to Taiwan to escape persecution and to reorganize for the struggle against the now-communist mainland. Due to their somewhat unrealistic world-view and the previous experience that the GMD had in statecraft, they dominated the native Taiwanese, establishing class distinctions and a industrial base very quickly in China.
This was aided by their closer connections with the western powers, established early on and kept up through WW2, for example. The communist mainland was forced to start from the ground up, more or less, receiving much less aid and having vastly greater problems of organization, due to size and the rural state of the population. Taiwan made quick, important gains in schools and infrastructure as well, reinvesting money with the purpose to make Taiwan rich.
Taiwan was, due to foriegn connections, especially with the USA, also the first and only representatives of Chinese people in the international community. They filibustered and protested very loudly whenever the CCP tried to gain voice in international forums like the UN, and insisted for a very long time that they(Taiwan) represented the entire land area inhabited and governed by the CCP. They had a thriving international lassiez-faire economy that also interested foreign powers in keeping the statist mainland from absorbing Taiwan.
Taiwan was also quick to arm, due to militaristic preoccupation and the threat of mainland China. For many years, possibly even today, China could not annex Taiwan without massive, debilitating effort, and would embroil itself in international conflict as well. China has by today become an industrial nation of the first tier, and the ‘cat theorist’ have brought it out of total isolation- to anger China now has economic ramifications, and thus they make it costly to interfere with their goals. Military action is a constant threat, but not likely unless a particular brand of revanche hard-line politics comes to power in Beijing.
Culturally, also, times have changed in fifty years. National identity has grown apart- enough mainlanders on Taiwan have given way to mixed generations, and the ‘pure’ mainlanders no longer run politics completely. So it will be very hard to re-establish a cultural over Taiwan again, should China r-gain control. The two governments are much the same vintage, and neither one has more precedent or experience than the other- they are truly separate states now. China now represents China in the UN, and Taiwan is not able or willing to present its claims to rule the mainland anymore.
China feels it must re-gain control of Taiwan and its rich industrial base, in order to augment its own resources and also to more thoroughly control the trade in the area. Japan and the US, the only real competition in the area, certainly don’t want that unless they have guarantees of free trade and so forth. The Taiwanese are certain that Chinese annexation would result in a great shift downward in their lifestyles and freedom, but they must heed the realities of the situation, globally and locally, which is that China is bigger, and has some claim to exercise, and will, given enough isolation and/or ignorance from the world, take over Taiwan.
The movement in Taiwan to open relations and dialogue with China is the only way the rich, capitalist Taiwan is going to influence events in the future. From the US perspective, it matters only if China redirects Taiwanese capital and business into China rather than allowing it to continue freely. The issue of trade control in SEasia is also a knotty problem- Taiwan may be seen as the boulder in the stream that splits and weakens the Chinese river of regional control.