8-10 minutes - Source: BBC
Police have used pepper spray to disperse some protesters gathered to mark 23 years since British rule ended.
The national security law targets secession, subversion and terrorism with punishments up to life in prison.
Critics say it stops some freedoms meant to be guaranteed by China.
Hong Kong's sovereignty was handed back to China by Britain in 1997, under an agreement designed to protect certain freedoms for at least 50 years.
The annual pro-democracy march to mark the anniversary had been banned for the first time by authorities, who cited a bar on gatherings of more than 50 people because of Covid-19.
Police confronted a small group of demonstrators gathered in the city centre and at least 30 people were arrested for "unlawful assembly, violating the security law, obstructing police and possession of weapons".
Those arrested included a man carrying a "Hong Kong Independence" flag - protesters have been warned certain slogans and banners might constitute serious crimes under the new law.
Earlier, Chief Executive Carrie Lam, the city's pro-Beijing leader, said the law would "restore stability" after widespread protests in 2019, saying: "The [new law] is considered the most important development in relations between the central government and Hong Kong since the handover."
The legislation has been widely condemned by countries including the US and UK as well as human rights activists and groups. US Secretary of State Mike Pompeo said: "[China] promised 50 years of freedom to the Hong Kong people, and gave them only 23."
But one Chinese official bristled at foreign critics, asking them: "What's this got to do with you?"
"We Chinese will not be scared by anyone," said Zhang Xiaming of the Hong Kong and Macau Affairs office of the State Council. "Gone are the days when we had to take cues from others."
Hong Kong's new security law
What is happening on the anniversary?Some pro-democracy activists have pledged to defy the ban and march later in the afternoon. "We march every year... and we will keep on marching," veteran Leung Kwok-hung told Reuters.
Photos on social media - confirmed by police as genuine - showed a flag being used to warn protesters about the new law.
One pro-democracy activist warned there was a "large chance of our being arrested".
"The charges will not be light, please judge for yourself," said Tsang Kin-shing of the League of Social Democrats.
Police officers in the city are on standby, insiders told the South China Morning Post. They said around 4,000 officers were poised to handle any unrest.
What does the new law say?Under the new law, crimes of secession, subversion, terrorism and collusion with foreign forces are punishable by a minimum sentence of three years, with the maximum being life.
Protesters often targeted city infrastructure during the 2019 protests, and under the new law, damaging public transport facilities can be considered terrorism.
Beijing will also establish a new security office in Hong Kong, with its own law enforcement personnel - neither of which would come under the local authority's jurisdiction.
Inciting hatred of China's central government and Hong Kong's regional government are now offences under Article 29.
The law can also be broken from abroad by non-residents, under Article 38. This could mean that foreigners could be arrested if they step into Hong Kong, if they are suspected of breaking the new law.
Some critics feared the law would apply retroactively - that is, to offences committed before the law was passed - but Mr Zhang said that would not be the case.
He added that suspects arrested in Hong Kong on charges of violating the law may be tried on the mainland.
Activists go quietUnder the national security law, many of the acts of protest that have rocked Hong Kong over the past year could now be classed as subversion or secession… and punished with up to life in prison.
Carrie Lam said the law was long overdue. Political activists have resigned and one pro-democracy protester, who asked to remain anonymous, told me that ordinary people were now deleting posts on social media.
Many people are just stopping talking about politics, and stopping talking about freedom and democracy, because they want to save their own lives. They want to save their freedom and avoid being arrested.
One contact of mine, a lawyer and human rights activist, sent me a message shortly after the law was passed. Please delete everything on this chat, he wrote
What reaction has the new law drawn?Mr Pompeo said the "draconian" law "destroyed Hong Kong's autonomy".
"Hong Kong demonstrated to the world what a free Chinese people could achieve - one of the most successful economies and vibrant societies in the world," he said.
"But Beijing's paranoia and fear of its own people's aspirations have led it to eviscerate the very foundation of the territory's success."
Meanwhile, Canada has updated its Hong Kong travel advice, saying: "You may be at increased risk of arbitrary detention on national security grounds and possible extradition to mainland China."
Minutes after the law was passed on Tuesday, pro-democracy activists began to quit, fearful of the punishment the new law allows.
"With sweeping powers and ill-defined law, the city will turn into a secret police state," said Joshua Wong, a key pro-democracy leader.
The political party he co-founded - Demosisto - was also disbanded.
One opposition legislator told the BBC the move had taken away the city's rights.
"Our freedom is gone, our rule of law, our judicial independence is gone," said Ted Hui.
In the US, lawmakers from both parties have launched a bill to give refugee status to Hong Kong residents at risk of persecution, reported local media outlets.
Taiwan's government has said it will set up a special office to help those in Hong Kong facing immediate political risks.