In the U.S. some heavyweight papers have published leader articles that are unprecedented in their contempt for the future president.
The New York Times says Mr Trump "is the most unprepared president-elect in modern history" and "has shown himself to be temperamentally unfit to lead a diverse nation of 320 million people."
The Washington Post sees little cause for optimism about the vote, recalling that Trump "has promised to deport millions, rip up trade agreements and international efforts to fight climate change, each of which would hurt many people".
The Los Angeles Times asks in its editorial "How did that happen?" The paper says "the campaign, and the candidate, played to the worst in America, and it has left the electorate scarred."
The Miami Herald says in an editorial: "The losers, still stunned, must acknowledge that Mr Trump managed to read the mood of much of the country better than they did, tapping into the frustrations of people who had come to believe that the government was no longer working on their behalf or even understood their problems."
European media are also stunned by Americans' choice.
"How could this happen?" is a headline on the website of German daily Die Welt. It says Trump is as "unpredictable as a hurricane."
The main German public service news program Tagesschau tries to provide an answer, saying Trump "owes his electoral victory mainly to white male voters" who voted for "the political outsider."
The French business daily Les Echos is forthright in its assessment: "Racist, populist, male chauvinist, arrogant and unpredictable. We do not know what is most terrifying in the personality of Donald Trump."
The Washington correspondent of Spain's El Pais stresses that Trump "goes to the White House with massive support from white voters discontented with elites".
Papers in Italy agree, with La Stampa seeing the result as "a hurricane of discontent" that comes "from the belly of the nation."
Russia's state-run rolling-news TV channel Rossiya 24 carried Trump's victory speech live instead of its 0800 gmt news bulletin. The station aired an animated graphic, showing Trump dancing ecstatically and making faces at Clinton, who is sitting despondently.
"The epic defeat of Hillary Clinton... is a resounding slap from the people to the U.S. political elite" is how the official Rossiyskaya Gazeta paper sees it. "No less resounding than the slap that Britons earlier gave to their authorities at the referendum on EU membership."
Chinese official commentaries say Trump's victory is a "major blow" to the U.S. establishment.
"From the start, mainstream U.S. media and elites looked down on Trump and described him as loose cannon," the Global Times says on its website.
"We cannot bank the future of Sino-U.S. ties on his character," the paper adds. "Ultimately, it depends on our own strength to maintain China's interests."
Latin American newspapers are surprised but also anxious about the news.
A front-page opinion piece on Argentina's Clarin calls Donald Trump "an emerging neo-fascist."
"The phenomenon is not a one-off," it continues. "It correlates with many European ultra-nationalist figures, and is growing at a serious moment for the world."