Michel Temer, Brazil's interim-president, has opened the Olympic Games, but was loudly jeered by some in the audience.
He spoke only briefly before declaring the Games open, initiating a fireworks display.
Mr Temer became the country's acting president after Dilma Rousseff was suspended awaiting a trial by the Senate.
Ms Rousseff did not attend the ceremony.
The refugee team, representing the 65 million displaced people around the world, have entered the Maracana stadium.
The team of 10 athletes was greeted with huge applause from onlookers.
The Rio Olympics is the first time a refugee team has competed in the Games
Team GB have taken to the Maracana stadium in Rio, led in by tennis champion Andy Murray.
Wearing red, white and blue, the squad soaked up the carnival atmosphere, with some taking selfies while all waved to the crowds.
"Who else got goosebumps", they asked in a Tweet.
The athletes of the 207 teams competing in the 2016 summer Olympics have made their appearance in the Maracana stadium.
As is traditional, Greece, the home of the Olympics, came in first, their flag carried for the first time by a female athlete.
In keeping with the environmental theme, each team is to be led out by a rider on a bicycle.
Amid the music and celebration, Brazil's opening ceremony has also included a sombre warning on climate change.
The serious segment began by examining the concentration of carbon dioxide on the planet.
It included the voice of British actress Judi Dench, who read an English translation of Carlos Drummond de Andrade’s poem, 'A Flor e a Náusea'.
The opening ceremony to the 2016 Olympic Games has got under way, lighting up the Maracana stadium in Rio de Janeiro.
The spectacular ceremony, which has so far retraced the history of Brazil and included dancing, capoeira displays and a performance of 'The Girl From Ipanema' - has as its themes were world peace and the environment.
Brazil's suspended President Dilma Rousseff has said she is "sad" that she will not be present at the opening ceremony of the Olympic Games.
Ms Rousseff, who was suspended from office in May pending a trial by the Senate on charges of breaking budget laws, said on her Twitter account she was "sad not to be at the party 'live and in colour' but I will be following it, rooting for Brazil".
Her suspension has played into Brazil's political turmoil, which has seen protests in Rio de Janeiro ahead of the Games.
Ms Rousseff turned down an invitation to the opening ceremony last month, saying she would not play second fiddle to her replacement, interim President Michel Temer, who will declare the Games officially open.
Police in Brazil have clashed with protesters ahead of the Rio 2016 opening ceremony.
Large crowds forced the Olympic torch relay away from its planned route through the city's Copacabana beach.
UN Secretary General Ban Ki-moon earlier ran with the torch by Ipanema beach after receiving it from International Olympic Committee President Thomas Bach.
The flame will be used to light the Olympic cauldron on Friday night at the Maracana Stadium.
Protesters were tear gassed during clashes with riot police just hours before the Olympic opening ceremony in the latest of a series of angry demonstrations around the Rio Games.
Thousands of police had to escort the Olympic torch on its journey to the stadium as demonstrations threatened to overshadow tonight's grand ceremony, reports ITV News Correspondent John Ray.
Protesters blocked the path of the torch relay as they accused the government of ignoring political and economic crises within Brazil.
Among those chanting angrily on the streets were supporters of Brazil's ousted left-wing president and campaigners highlighting the deep split between rich and poor amid a serious recession.
"In the real Rio de Janeiro that is not on the postcards people are angry because we have a lot lacking and the government is choosing to not see," said student protest leader Gabriel de Melo.
At Copacabana beach the Olympic party was forced to dodge protests by extinguishing the iconic torch and hiding the flame in a small lamp.
However, the calls for change might be harder to avoid.
The details of tonight's Olympics opening ceremony have been tightly guarded - but one certainty is that it will be an extraordinary show.
Rio is used to putting on party and watchers can expect a taste of carnival tonight, reports ITV News Sports Editor Steve Scott.
Tens of thousands of people joined open auditions in an attempt to be a part of the grand opening.
And samba schools, dancers and costume fitters have been among those busily practicing ever since.
Performer Ernesto Magalhaes said watchers could expect "a bit of a mix".
"People will get to know a little bit of our history but they will also know about modern Brazil and our popular culture," he said.