Russian President Vladimir Putin has declared the Sochi Winter Games officially open.
40,000 spectators attended the opening ceremony at the new Fisht Stadium.
Mr Putin and leaders from China, Japan and about 40 other countries clapped as athletes emerged from beneath the stage up a ramp for the traditional parade.
A giant satellite image of each nation taken from space was projected onto the floor.
The ceremony got off to a shaky start when one of the five Olympic rings failed to open, meaning the symbol could not be illuminated with fireworks as planned.
The state-of-the-art Fisht arena is one of several construction projects that have swelled the budget of the Winter Games to a record $50 billion (€37bn).
The run-up to the Games has been marred by threats from Islamist militants based in nearby Chechnya and neighbouring southern Russian regions to launch attacks.
In Turkey, special forces today seized a suspect who made a bomb threat and tried to hijack a passenger plane demanding to go to the Winter Olympics venue of Sochi.
There has also been international criticism of Russia's new "gay propaganda" law.
Organisers have been under fire for the huge costs involved, unfinished accommodation and amenities, and even the treatment of stray dogs in and around Sochi.
Google doodle flies gay flag for Winter Games
Google placed a rainbow version of its logo on its search page today, increasing pressure on Mr Putin over his country's "gay propaganda" law at the Sochi Winter Olympics.
The page showed a winter sports competitor above each of the six letters in the US internet giant's name, set against backgrounds in the six colours on the gay pride flag.
The page also included a quote from the Olympic charter underlining the right to practice sport without discrimination.
"The practice of sport is a human right. Every individual must have the possibility of practicing sport, without discrimination of any kind and in the Olympic spirit, which requires mutual understanding with a spirit of friendship, solidarity and fair play," it says.
Google did not immediately comment.
The international outcry over the law, signed by Mr Putin last year, threatens to undermine his hopes of using the Games to portray Russia as a modern state that has come a long way since the Soviet Union collapsed in 1991.
Mr Putin says the legislation, banning gay propaganda among minors, is needed to protect young people.
Critics say it fosters a climate of discrimination against lesbian, gay, bisexual and transgender (LGBT) groups.
Telecoms company AT&T, a sponsor of the US Olympic team, criticised Russia this week over the law, increasing pressure on other companies to speak out.
The Human Rights Campaign, an LGBT rights organisation, praised Google for what it called a move to show solidarity with LGBT Russians and visiting athletes.
"Google has once again proven itself to be a true corporate leader for equality," HRC President Chad Griffin said.
"Alongside Olympic sponsors like AT&T, Google has made a clear and unequivocal statement that Russia's anti-LGBT discrimination is indefensible.
"Now it's time for each and every remaining Olympic sponsor to follow their lead. The clock is ticking, and the world is watching."
Companies including McDonald's, Coca-Cola and Procter & Gamble pay around €74m each for rights to sponsor the Olympics over a four-year period and want to tap into a feel-good atmosphere during the Games.
These companies are also facing pressure to speak out over the "gay propaganda" law.
"These brands have spent millions to align themselves with the Olympics, but have repeatedly refused to support the founding principles of the Games," Andre Banks, one of the founders of gay rights group All Out, said earlier this week.
United Nations Secretary-General Ban Ki-moon condemned sexual discrimination and attacks on homosexuals in a speech to the International Olympic Committee in Sochi yesterday, which also drew attention to Russia's record on gay rights.
Deputy Prime Minister Dmitry Kozak said shortly afterwards in Sochi that there would be no discrimination at the Games.
"We're all grown-ups and every adult has the right to understand their sexuality," Mr Kozak said.
But, echoing a remark by Mr Putin, he added: "Please do not touch kids."