As of now they are basically independent except that China doesn't acknowledge it and many countries acknowledge there being one China. However, eventually it will be to the best interest of the Chinese people as a whole to reunite and thus making "China" stronger. Many Chinese hope for this and signs are showing that it is inevitable that the Chinese people will be united again. For example the economics many Taiwanese companies are outsourcing to China as it is cheaper, the communist government in China is a dying legacy and is being replaced by more "western" economic and open minded leaders, and the sentiment of most people is for reunifcation. I think perhaps the only people that would oppose eventual, not immediate, reunification would be the Taiwanese of aboriginal descent. They were there before the Nationalists fled communist China and are considered truely Taiwanese and would be the only ones who truely oppose unification and advocate independence.
Anyways...that's how I see it. I'm Chinese and my parents are from Taiwan. Also, if China and Taiwan were to go to war Taiwan could not last more than a week without immediate US military intervention.