Media playback is unsupported on your device Media caption Key moments: Republican contenders for the US presidency have been taking part in their second live TV debate

Donald Trump has come under attack from all sides in a fiery debate between the top Republican presidential candidates in the 2016 election.

The party's frontrunner, a billionaire businessman with no political experience, refused to apologise over comments about the wife of Jeb Bush.

And he was on the receiving end when Carly Fiorina drew huge applause facing up to his recent jibe over her looks.

Fifteen Republicans are vying to be the party's White House nominee in 2016.

With more than a year until polling day, the second Republican debate in the Ronald Reagan Presidential Library in California saw Mr Bush and Mr Trump trading blows several times.

Image copyright Getty Images Image caption Carly Fiorina, above with John Kasich, performed well

Image copyright Reuters

Their most notable clash in the debate, hosted by CNN, came when the former Florida governor demanded that the tycoon apologise to his wife for saying he was weak on immigration because she is Mexican. Mr Trump refused.

But the loudest audience response of the night came when Ms Fiorina was asked about an interview in which Trump said she could not be president because "Look at that face".

She replied, to thunderous applause: "I think women all over this country heard very clearly what Mr Trump said."

Mr Trump's exchange with Mr Bush:

JB: "To subject my wife into the middle of a raucous political conversation was completely inappropriate and I hope you apologise for that Donald."

DT: "Well, I have to tell you I hear phenomenal things, I hear your wife is a lovely woman. I don't know her."

JB: "She is, she's fantastic. She is absolutely the love of my life, and she's right here, and why don't you apologise to her right now?"

DT: "No, I won't do that because I said nothing wrong, but I do hear she's a lovely woman."

Media playback is unsupported on your device Media caption In their second TV debate, Carly Fiorina rebuked Donald Trump for his recent comment that voters might not back her because of her looks.

Mr Trump's exchange with Ms Fiorina:

Moderator Jake Tapper gives Ms Fiorina the chance to respond to Mr Trump's comments about her in Rolling Stone magazine in which he said: "Look at that face. Would anyone vote for that. Can you imagine that as the face of our next president?" Mr Trump later said he was talking about her persona, not her appearance.

CF: "You know it's interesting to me. I think women all over this country heard very clearly what Mr Trump said."

(Loud applause)

DT: "I think she's got a beautiful face and I think she's a beautiful woman."

But if Mr Trump predictably took plenty of punches, as the candidate who has held a commanding lead for much of the campaign, he gave as good he got throughout the debate in his trademark style.

He returned fire on Kentucky Senator Rand Paul with an oblique personal insult about his appearance, mocked the fiscal record of Wisconsin Governor Scott Walker and introduced himself with the words: "I say, not in a braggadocious way, I've made billions and billions of dollars."

Other highlights in the debate:

Mr Bush said the UK's former prime minister, Margaret Thatcher, should have her face on the $10 bill

Ms Fiorina said women's health organisation Planned Parenthood should be denied all state funding, even if it triggers a government shutdown

the only woman in the field also attacked the record of the Democratic frontrunner Hillary Clinton

Chris Christie said Mrs Clinton should be prosecuted for using a private email server

Marco Rubio and Mr Bush defended speaking Spanish on the campaign trail, after criticism from Mr Trump

Mr Bush admitted smoking pot in his youth, while Rand Paul took flak for defending legal marijuana

the Kentucky senator also said he would not send US troops back to Iraq to fight Islamic State militants

Ben Carson, second in the polls, had a quiet night

Ted Cruz said he was the only candidate not backing amnesty for illegal immigrants

At the scene: Jon Sopel, BBC North America editor

And so it was in the beautiful Simi Hills in California last night at the Ronald Reagan Presidential Library that the Republican candidates took it in turn to try to give Donald Trump a bloody nose, a cracked rib, a thick lip and black eye.

Ideally all four at once.

First up, flexing his muscles, and jabbing hard, was Senator Rand Paul on whether Trump had the character to have his hand on the nuclear trigger.

Read more from Jon Sopel: Has Fiorina found Trump's kryptonite?

Republican debate's winners and losers

Twists and turns of debate as they happened

Join in our debate on Facebook

A second-tier debate for the four other Republican candidates happened on the same stage earlier.

In a combative atmosphere, the four were split over the case of Kim Davis, a Kentucky clerk jailed for refusing to issue marriage licences to gay couples due to her Christian faith.

The Democratic Party will hold its first debate in Nevada in October, also hosted by CNN.

Iowa will be the first state to choose its candidate from each party on 1 February, and is seen as a key indicator for the race ahead. Other states hold primaries in the following weeks and months.

By next summer, each party will have a presidential nominee who will do battle in the race for the White House.

Votes will finally be cast in November 2016.

2016 hopefuls

Image copyright AP Image caption Clockwise from top left: Donald Trump, Jeb Bush, Scott Walker, Marco Rubio, Bernie Sanders, Hillary Clinton

The early Republican frontrunner is Donald Trump

Hillary Clinton will have learnt much from her failed campaign of 2008

Florida senator Marco Rubio lost some right-wing fans by backing a bipartisan immigration reform package

Wisconsin governor Scott Walker appeals to both the Republican establishment and the Tea Party

Libertarian Rand Paul has his supporters - and enemies - among Republicans

Veteran congressman Bernie Sanders is drawing huge crowds at his rallies

Meet all of the 2016 hopefuls