Anthony Zurcher
BBC North America reporter

Image source, Getty Images

"This was a speech for the angry, the frustrated, the American voters who turned out in places like Pennsylvania, Michigan, Florida and Ohio to shake their fist at the status quo and take a chance on a man who was unlike any presidential politician who came before him.

It should also serve as a wake-up call to American allies, as Mr Trump insisted that the US will put its own interests first both economically and militarily.

The challenge now will be to live up to his rhetoric as a different kind of president - and bring the rest of the nation along with him on the journey."

Read Anthony's analysis in full

Here are some of the best clips from the Trump inaugural...

Trump is attending a luncheon at Congress, but before beginning his meal, he took his first actions as president.

He signed into a law a waiver to allow Defense Secretary-designate James Mattis, a retired US Marine Corps general, to serve, Trump's spokesman said. 

Mattis requires a Senate waiver, since former service members are required to be out of uniform for over seven years to become Defence Secretary.

He also formally sent his cabinet nominations to the Senate, and called for a national day of patriotism. 

Image source, Getty Images

And for those who may have missed it, here's the full text of Trump's inauguration speech.

Image source, EPA

Donald Trump begins his presidency with a far lower approval rating than his three predecessors. Can he turn that around?

In the weeks and months to come, we'll be tracking the progress he makes on his agenda and how it is received by the American public.  

Image source, Getty Images

UK Foreign Secretary Boris Johnson has congratulated President Donald Trump on taking office, saying Britain will work "hand and glove" with him for the "stability, prosperity and security of the world". 

"I want to offer my warmest congratulations to President Donald Trump on acceding to the most important political office in the world and I know that billions of people will be willing him to succeed in the months and years ahead, in the very great challenges that he faces," Johnson said.

Image source, AFP

The BBC's Rajini Vaidyanathan is on the National Mall, speaking to supporters who just witnessed Donald Trump being sworn in as president.

See what they have to say about the atmosphere in Washington today.

A spokesman for former President George HW Bush, 92, says he and his wife Barbara, 91, son Neil, and daughter-in-law Maria were watching the inauguration ceremony from Houston Methodist Hospital in Texas. 

Mr and Mrs Bush were both admitted to hospital earlier this week due to dizziness and breathing issues. 

In a letter to President Trump, Mr Bush wrote that "my doctor says if I sit outside in January, it will likely put me six feet under".

"Same for Barbara. So I guess we're stuck in Texas," he wrote. 

His son, former President George W Bush, sat on the dais during the inaugural ceremony.

Some more photos of all the day's action here.

Image source, Epa

Image source, EPA

Image source, Getty Images

Image source, Reuters

Image source, Reuters

Compare crowd at Obama's 2009 inauguration (top picture below) with Trump's...

More than 1.8 million people are estimated to have attended Obama's first swearing-in.

There are no official crowd estimates yet for Trump today.

Image source, Getty Images

The website impeachdonaldtrumpnow.org, external has just gone live.

The organisers behind the campaign, Free Speech for People, external and RootsAction, external, cite Trump’s ownership of his luxury hotel and golf course businesses while in office.  

They allege this is a conflict of interest and an ethics violation.

Read up on all of Trump's potential conflicts of interest here:

Donald Trump: A list of potential conflicts of interest

As former President Obama speaks, Donald Trump signs orders for formal Cabinet nominations and a proclamation for a national day of patriotism, his spokesman says.

"Michelle and I have been really milking this goodbye thing," says Obama.

He says he and Michelle were just the "frontman and frontwoman" of the movement.

"Yes we did!" Obama says as he leaves.

Despite the naysayers, "all of you came together, in small towns and big cities, a whole bunch of you really young, and you decided to believe".

He praises those who campaigned for him and explained to their "parents how to pronounce Barack Obama".

"This has been the privilege of my life." 

Tara McKelvey
BBC News, White House correspondent

"Once President Trump started speaking, hundreds of people - many wearing Trump hats - started heading out in the Silver Ticket section. Some said they were hungry or wanted coffee. But still it was surprising to see so many people leave during the speech." 

Trump ally Roger Stone has taken to Twitter to air some grievances, and pat himself on the back.

Check out his top hat and three-piece suit.

"When we started on this journey, we did so with an abiding faith in the American people and their ability, our ability, to join together and change the country."

We knew that "change didn't happen from the top down, but the bottom up".

"Yes we did!" a crowd is shouting for Obama, as he lands at Andrews Air Force base. 

The former first couple are listening to the national anthem with their hands held over their hearts. 

New York Magazine editor Kyle Buchanan notes the background photo of the new Donald Trump presidential Twitter account - crowds waving flags in front of the Capitol building - is actually a photo from Barack Obama’s 2009 inauguration.

Some have noted that crowds were somewhat sparser at today's Trump swearing-in, compared with Obama's. 

Former veep Joe Biden is now travelling in somewhat less grander style.

He and his wife, Jill, have just boarded an Amtrak train which will take them to their home state of Delaware.

Biden, who served for decades as a US senator, famously liked riding the train into DC every morning, rather than live in the capital city itself.

The ride is just about two hours in each direction.