Pretty much all of their claims to the SCS and many of their border claims on the continent. Their border claim is the maximum extent at any point in time of any chinese border, not at any single point in time, any point in time throughout Chinese history. The current Arunachal Pradesh situation is a prime example too, they recently went from unofficial to official by expanding their claims there.
Not quite true. China doesn't claim everything that's ever been part of a Chinese (or China-centred, e.g. the Mongol & Qing/Manchu empires) state. For example, it recognises the independence of Mongolia, & the land borders (more or less) of Vietnam, despite all of Mongolia & the northern half of Vietnam having been part of China-centred empires at times. Nor does China claim Tuva, which was part of the Qing Empire.
But the Chinese claim to most of Arunachal Pradesh is completely spurious. It's based on exaggerated Chinese claims of what where the borders of Tibet, at a time when Tibet was not under Chinese control, but a pretty much independent state with a Manchu official & small retinue in Lhasa, but no Chinese authority elsewhere in the country. These territories had been ruled by Tibet in the distant past, when it was a completely independent country, able to invade China & sack its capital, but were lost over 1000 years ago.
The claim to Tibet is based on it being part of the Mongol & Manchu empires, but this is a very fragile basis. Apart from the obvious factor of self-determination, it ignores the nature of both Mongol & Manchu rule. The Mongol link is easily dismissed: Tibet was no more part of China to the Mongols & their Chinese subjects than, e.g, Iraq or S. E Russia. Any claim to Tibet based on Mongol rule would apply equally to all former Mongol-ruled territories. The Manchu situation is more complicated, but AFAIK the Manchus invaded to throw out Mongol invaders, & then made Tibet a protectorate (not directly administered) of the Manchu empire, not part of China. It was self-governing, with only the previously mentioned official resident. The relationships was similar to that of Nepal to the UK, which ended with Nepal becoming an independent state when the British Empire broke up, not part of another former British subject territory (India). The Qing intervened a couple of times, but their interest was in propping up Tibet, not ruling it. They helped Tibet repel invasions, & tried to make sure the government was stable & friendly.
The Manchus sent in Chinese troops after the British invasion of 1904, but they were treated (& acted) as invaders, not as defenders against foreign invasion. Soon afterwards, the fall of the Manchu dynasty broke the link: Tibet declared its independence & was left to it by the new Chinese republic. It was effectively fully independent until 1949.
The claims in the South China Sea are a mess. All the littoral states make exaggerated claims, but China's are the most exaggerated. The only hope for a conclusion that I can see is for the country with most clout to lay out reasonable, sensible, proposals. That'd lead to outsiders putting pressure on the other littoral states to stop complaining & agree. But as long as China refuses to renounce the nine-dashed line, there won't be progress.