After decades of hostile intentions and angry rhetoric, relations between China and Taiwan started improving in the 1980s. China put forward a formula, known as "one country, two systems", under which Taiwan would be given significant autonomy if it accepted Chinese reunification. The offer was rejected, but Taiwan did relax rules on visits to and investment in China. It also, in 1991, proclaimed the war with the PRC over.
There were also limited talks between the two sides' unofficial representatives, though China's insistence that the ROC government is illegitimate has prevented government-to-government contacts.
Progress since then has been limited. China began worrying that former Taiwanese President Lee Teng-hui was inching the island towards formal independence. Beijing became even more alarmed in 2000, when Taiwan elected as his successor Chen Shui-bian, who had openly backed independence.
China responded by saying it was ready for more talks, but only if President Chen accepted Beijing's 'one China' position, a concession he was never likely to accept.
Mr Chen was re-elected in 2004, prompting Chinese concern that his pledge to rewrite the island's constitution would edge it towards formal independence.
Partly to limit his options, China passed a so-called anti-secession law in 2005, stating China's right to use "non peaceful means" against Taiwan if it tried to secede from China.
While political progress has been slow, links between the two peoples and economies have grown sharply. Taiwanese companies have invested more than $50bn in China, and up to 1m Taiwanese now live there, many running Taiwanese factories.
Some Taiwanese worry their economy is now dependent on China. Others point out that closer business ties makes Chinese military action less likely, because of the cost to China's own economy.