Millions of people around the world lined waterfronts and filled city squares last night to welcome in 2015 with spectacular firework displays as well as traditional events – but celebrations in Shanghai were marred by tragedy, as dozens of revellers were killed and injured in a stampede.

According to Chinese state media, at least 35 people were killed and 42 injured in the crush, which happened in the city’s Bund riverfront area at about 11.30pm local time. Emergency services soon arrived to aid the wounded in Chen Yi Square, an area that often becomes crowded during major events. It was not immediately clear what triggered the stampede.

The official Xinhua news agency said many of the injured were students. Photographs on Weibo, the Chinese version of Twitter, showed densely packed crowds of revellers along the Bund, which lies on the bank of the Huangpu river. In some photographs, rescue workers were seen trying to resuscitate victims on the pavement while ambulances waited nearby.

Authorities had shown concern about crowd control in the days leading up to New Year’s Eve. They recently cancelled an annual 3D laser show on the Bund which attracted 300,000 people last year.

New Zealand, the first country to celebrate the new year, celebrated with fireworks launched from Auckland’s Sky Tower, while in Australia an estimated 1.5 million spectators lined the harbour to watch the now renowned firework display on Sydney Harbour Bridge. The event, broadcast to an estimated billion people, featured a tribute to the two hostages killed in the December siege inside a cafe before seven tonnes of fireworks, including 10,000 aerial explosives and 100,000 pyrotechnics, went up in smoke.

In Indonesia, celebrations were muted because of the recent loss of AirAsia Flight 8501. In Japan, people filled temples and shrines to pray for peace as bells struck 108 times to mark the number of temptations in Buddhism.

Dubai saw hundreds of thousands of revellers watch fireworks launch from the Burj Khalifa, the world’s tallest building, which was wrapped with 70,000 panels to create the biggest ever illuminated LED facade. Meanwhile, a light show and fireworks marked the beginning of 2015 at the Olympic park in Beijing.

Moscow was one of the first cities in Europe to mark the new year, with fireworks detonating over St Basil’s Cathedral and the Kremlin.

In London, 100,000 people gathered on the banks of the Thames to watch an 11-minute firework display involving 12,000 pyrotechnics. This year’s event was ticketed for the first time, with revellers paying £10 each to access the fenced-off viewing area, after around half a million tried to squeeze into the area around the South Bank last year.

“If you don’t have a ticket, the best place to watch the #londonnye fireworks will be live on the BBC,” the office of the London mayor, Boris Johnson, said on Twitter after telling the public that last year’s crowded conditions meant that a free event was “untenable”.

However, he came under fire from opposition politicians over the ticketing and for the erection of mobile signs hammering home the message that the fireworks were being shown on the BBC. Fiona Twycross, a member of the London Assembly, described the signs as an insult to Londoners and visitors to the city and accused the mayor of privatising New Year by bringing in the ticketing system.

Those who bought tickets, however, described the atmosphere as “electric”.

In Scotland, Hogmanay celebrations on Stirling Castle’s esplanade were cancelled due to high winds. A live outdoor concert had been due to take place on the esplanade, with music from The Waterboys, Skerryvore, JJ Gilmour and Model Aeroplanes, followed by a fireworks display. However, the event was cancelled as high winds meant public safety could not be guaranteed, police said.

Chief Inspector Paul Rollo, Stirling policing commander, said: “Hogmanay is one of the highlights of the year in the city, and the joint decision to cancel the street party was only taken after lengthy discussion and deliberation with the organisers.

“We prioritise the safety of people attending an event and with the poor weather conditions right now with winds far stronger than expected, unfortunately this could not be assured.”

Up to 75,000 people were expected to gather for the world-famous event in Edinburgh, which saw Lily Allen headlining the Concert in the Gardens. There were five live stages throughout the city, with 13 acts performing, including Soul II Soul and Twin Atlantic, plus four firework displays.

Early celebrations included a torchlight parade when a cast of thousands carried flaming torches through the historic Old Town. Organisers said tickets for events have been bought by those in more than 70 countries, including Australia, Brazil, Mauritius, Slovakia and South Africa.

Wilson Peery, 33, from Oregon, USA, travelled to Scotland especially to attend Edinburgh’s street party. He said: “I came here in 2008 and made a split second decision to come back this year with a group of friends. We all just decided to come.

“I just really like the energy and the fact that there are so many things to do. The torchlight procession is something special.”

As the new year reached Rio De Janeiro, millions flocked to Copacabana beach, where fireworks were launched from boats and artists and DJs performed on three stages for a traditional all beach party where many revellers wear white.

In Havana, people roasted pigs for their traditional New Year’s Eve family dinners, often using a pit dug in the backyard.

And in New York, thousands gathered in Times Square to see in 2015 and watch the traditional dropping of a giant crystal ball at midnight. Extra police were drafted in in case of possible further protests following the deaths of two unarmed black men at the hands of police officers in the city and in Ferguson, Missouri.