In 2013, the Philippines asked the Permanent Court of Arbitration to declare invalid most of China's maritime claims in the disputed area.
China claims almost the whole of the South China Seaangering several Asian neighbours.
It says the tribunal does not have the jurisdiction to hear the challenge.
If the tribunal decides it can rule on the case, the legal hearings will get under way.
The Philippines has sent a high-profile legal team to the proceedings by the five-member tribunal which will continue till 13 July. China is not participating in the arbitration.
Vietnam, Taiwan, Malaysia, Brunei and Indonesia also have claims in the 3.5 million-sq-km (1.4 million-sq-mile) area said to be rich in resources.
The Philippines has had diplomatic spats with China over the Scarborough Shoal and Spratlys in particular.
It say China's "nine-dash line", which China uses to demarcate its territorial claims, is unlawful under the UN Convention on the Law of the Sea, which both countries have signed, and wants the tribunal to declare it invalid.