US election: Donald Trump promises a 'safer' America
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Trump: US 'in crisis'
Donald Trump has vowed to tackle multiple threats facing the US, in his speech in Cleveland, Ohio accepting the Republican presidential nomination.
"The crime and violence that today afflicts our nation will soon come to an end," he told the party convention.
The businessman promised his presidency would usher in a new era putting America and ordinary people first.
Mr Trump's nomination has been clouded by the refusal of major party figures like Senator Ted Cruz to endorse him.
Mr Cruz, who was his bitter rival during the primary contests, was booed off the stage by Trump supporters.
Other Trump opponents such as members of the Bush family stayed away from the convention altogether.
Mr Trump, a New York businessman who was written off when he launched his campaign a year ago, said he hoped his speech would ease tensions and unite the party.
Beyond the base - Anthony Zurcher, BBC North America reporter
Despite all the darkness of the opening and the rawness of Mr Trump's tone, his speech made a determined effort to expand his appeal beyond the angry white, working-class voters who make up the core of his support.
He reached out to black people - talking about their high levels of unemployment and poverty. He said the Obama administration had failed the inner cities on education, jobs and crime.
If Mr Trump's law-and-order pitch is to be successful, it cannot only be to his base - and this was a speech that acknowledged this.
In addition, Mr Trump once again went off-script when he spoke about protecting gay Americans from "violence and oppression of a hateful foreign ideology". It was a decided change in tone from a Republican nominee - and a stark contrast even from the platform his own party adopted just days earlier.
Speaking for well over an hour, he said the security of the country was under threat from Islamist radicals, undocumented immigrants and trade deals that failed American workers.
"We will lead our country back to safety, prosperity, and peace," he said. "We will be a country of generosity and warmth. But we will also be a country of law and order."
Addressing the "forgotten Americans" who worked hard but no longer had a voice, he said: "I am your voice."
Motherhood key theme of Ivanka Trump speech
He attacked his Democratic rival, Hillary Clinton, at every opportunity, blaming the former secretary of state for "death, destruction and weakness".
In a speech he described as a plan to "put America first", Mr Trump:
Promised to build a "great border wall" to stop illegal immigration, gangs and drugs
Accused Mrs Clinton of proposing mass amnesty, mass immigration and mass lawlessness
Said that decades of immigration have produced lower wages for African Americans and Latinos
Accused President Barack Obama of failing US inner cities on education, jobs and crime
Said that nearly 180,000 illegal immigrants with criminal records were "roaming free" to threaten citizens
Promised to end trade deals that had "destroyed [America's] middle class"
Promised that "Americanism, not globalism" would be the tenet of foreign policy
He was introduced in glowing terms by his daughter Ivanka, who said her father valued women workers and that he would make quality childcare affordable.
Not long into his speech, the audience began calling for the jailing of Mrs Clinton, chanting "Lock her up!" He promised to defeat her in November.
Balloons marked the end of the speech
This was a more sober Trump - no jokes and largely wedded to the teleprompter
What Republican delegates said about Trump's wall before the election
In a departure from Republican orthodoxy, Mr Trump took up the theme of acceptance of gay rights, framing it in terms of American values.
"I will do everything in my power to protect our LGBTQ citizens from the violence... of the hateful foreign ideology," he said to some cheers from the crowd.
"As a Republican it is so nice to hear you cheering for what I just said," he added.
In a key moment earlier in the night, Silicon Valley mogul Peter Thiel told the convention he was proud to be gay.
The chairman of the Hillary for America campaign, John Podesta, attacked Mr Trump's speech as divisive.
"Tonight, Donald Trump painted a dark picture of an America in decline," he said.
"And his answer - more fear, more division, more anger, more hate - was yet another reminder that he is temperamentally unfit and totally unqualified to be president."
Texas Senator Mr Cruz caused a storm on Wednesday night when he pointedly refused to back the nominee, sparking outrage and boos.
The moment the crowd turned on Ted Cruz
He later defended his decision, saying he would not be a "servile puppy" to someone who had attacked his family.
Mr Trump has previously criticised the appearance of Mr Cruz's wife, Heidi.
The nomination of the hotel developer has been a source of conflict within the party, with some like Mr Cruz questioning his conservative principles.
Others like former nominee Mitt Romney are concerned about his strident tone and extreme stance on immigration.