The US vetoed a resolution that would have required President Donald Trump to rescind his declaration of Jerusalem as the capital of Israel.
Nations began signing the first treaty to ban nuclear weapons, a pact backed by over 100 countries but rejected by those with nuclear arms.
Tough global challenges from the nuclear threat in North Korea to the impact of climate change will dominate discussions at this year's UN assembly.
The UN Security Council unanimously approved a resolution backing Gambia's new President Adama Barrow and calling on Yahya Jammeh to step down.
The world has made great progress in eliminating inequality between men and women in health and education.
The UN has urged international donors and the business community to contribute $100-million a year to combat a global pandemic of violence against women.