how is taiwan linked to china today

Taiwan used to be named Formosa and was part of what we now call mainland China. Here is a collection of websites that include this history:
http://www.google.com/search?q=taiwan+history&rls=com.microsoft:en-us:IE-SearchBox&ie=UTF-8&oe=UTF-8&sourceid=ie7&rlz=1I7SUNA

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Today, the relationship between Taiwan and China is complex and contentious. Taiwan is officially known as the Republic of China (ROC) and operates as a separate entity from the People's Republic of China (PRC), which is commonly referred to as mainland China.

Historically, Taiwan was ceded to Japan in 1895 after the First Sino-Japanese War and remained under Japanese rule until the end of World War II in 1945. After Japan's surrender, control of Taiwan was transferred to the ROC. However, the Chinese Civil War between the Kuomintang (KMT) and the Communist Party of China (CPC) was still ongoing. The CPC eventually defeated the KMT, and in 1949, the KMT retreated to Taiwan and established their government there.

Since then, Taiwan has developed its own government, economy, and military separate from mainland China. However, the PRC considers Taiwan to be an integral part of its territory and has not renounced the use of force to achieve reunification. Consequently, Taiwan is diplomatically isolated, with only a few countries officially recognizing it as a separate country.

Despite the political tensions, there are economic and social ties between Taiwan and China. Many Taiwanese companies have invested in China, and there is significant trade between the two regions. People from Taiwan also travel to China for business, tourism, and to visit relatives. Additionally, the two regions have cultural and historical connections dating back centuries.

It's important to note that the topic of Taiwan's status and its relationship with China is highly debated and can be sensitive. Therefore, understanding multiple perspectives and sources is crucial for a comprehensive understanding of the topic.