It is the first genocide case the International Court of Justice will hear in full in more than a decade.
The outcome will have repercussions beyond Myanmar, likely affecting South Africa's genocide case at the ICJ against Israel over the war in Gaza.
Myanmar has denied accusations of genocide.
"The case is likely to set critical precedents for how genocide is defined and how it can be proven, and how violations can be remedied," head of the UN's Independent Investigative Mechanism for Myanmar Nicholas Koumjian told Reuters.
The predominantly Muslim West African country of Gambia filed the case at the ICJ - also known as the World Court - in 2019, accusing Myanmar of committing genocide against the Rohingya, a mainly Muslim minority in the remote western Rakhine state.
Myanmar's armed forces launched an offensive in 2017 that forced at least 730,000 Rohingya from their homes and into neighbouring Bangladesh, where they recounted killings, mass rape and arson.
A UN fact-finding mission concluded the 2017 military offensive had included "genocidal acts".
Speaking in The Hague before the hearings, Rohingya victims said they want the long-awaited court case to deliver justice.
"We are hoping for a positive result that will tell the world that Myanmar committed genocide, and we are the victims of that and we deserve justice," Yousuf Ali, a 52-year-old Rohingya refugee who says he was tortured by the Myanmar military, told Reuters.
Myanmar authorities rejected that report, saying its military offensive was a legitimate counter-terrorism campaign in response to attacks by Muslim militants.
In the 2019 preliminary hearings in the ICJ case, Myanmar's then leader, Aung San Suu Kyi, rejected Gambia's accusations of genocide as "incomplete and misleading".
The hearings at the ICJ will mark the first time that Rohingya victims of the alleged atrocities will be heard by an international court, although those sessions will be closed to the public and the media for sensitivity and privacy reasons.
In total, the hearings at the ICJ will span three weeks.
The ICJ is the UN's highest court and deals with disputes between states.
Myanmar has been in further turmoil since 2021, when the military toppled the elected civilian government and violently suppressed pro-democracy protests, sparking a nationwide armed rebellion.
The country is currently holding phased elections that have been criticised by the United Nations, some Western countries and human rights groups as not free or fair.
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