Disclaimer: I am a Filipino poster, but I am of Chinese ethnicity. I'm just calling it as I see it based on my knowledge of international law.

If we're going to go by the Nine-Dash Claim then quite frankly the claims are a whole bunch of nonsense.

First of all, territorial waters are only supposed to extend 12 nautical miles from a nation's coast line. To claim the South China Sea would require China to massively increase this internationally agreed limit. Even using the Exclusive Economic Zone definition - which extends 200 nautical miles from the coast, simply isn't enough to cover the South China Sea. At this point China's attempt to claim the entire sea already falls apart. Here is a map showing the Exclusive Economic Zone limits versus China's claim to the entire South China Sea:

http://globalnation.inquirer.net/files/2014/03/South-China-Sea.jpg

However, some "geniuses" in China claim to have unearthed ancient documents that "prove" that the South China Sea was always Chinese along with the Spratley Islands. The problem is that these map actually date only from 1947, published by the Republic of China (Taiwan). Additionally, the Nine-Dash line is reliant on using reefs as the basis for extending territorial waters; which isn't recognized by international law.

Unfortunately certain Chinese officials were apparently undeterred by the legal impossibilities, and instead had the reefs expanded using concrete until they could be considered real "islands" that could be considered for the purpose of counting territorial waters. This was why there was all this recent concern about Chinese construction in the South China Sea.

At this point the Philippines decided to literally take the Chinese to court at the UNCLOS (United Nation Convention on the Laws of the Seas) to stop the Chinese plans. And the Philippine team, to a lot of people's surprise, are actually winning the case handily at this point; by focusing on the "ownership" of a number of reefs in the Spratleys (e.g. Scarborough).

To elaborate, the Philippine government showed the records of several ships which were wrecked on these reefs in the late 1800s - and how all of them chose Manila (capital of the Philippines) as the court of arbitration when it came to resolving the insurance claim. These records were verified by neutral third parties (e.g. Lloyd's of London, which handled the insurance claims).

Hence, the Philippine government had demonstrated that they they were already exercising legal jurisdiction over the disputed reefs since the late 1800s, or decades before the Nine-Dash Map was published.

Had China really been serious about owning these reefs, then it should have filed complaints back in the 1800s protesting the arbitration in Manila courts. They never did, and thus by extension waived their own jurisdiction. And if you don't have jurisdiction over a piece of land, you certainly can't claim to have sovereignty over it.

This was why the general Chinese reaction to the hearings had been to snub it entirely and called for a return to negotiations. They knew they had been completely outfoxed on the legal front. That doesn't mean China is going to stop trying however; but it's certainly more cautious now as it does not want to be seen as breaking international law.

Edit: Added a map.