Burnham appeared to make it through his crucial first meeting with Trump unscathed, but is the people-pleaser PM prepared to stand up to the President?

On this week’s Talking Politics, Tom and Robert are joined by Political Correspondent Romilly Weeks, hot off the prime minister’s plane back from New York.

Romilly tells us how she managed to catch Trump’s eye to ask him a question, and reveals the advice Burnham was given on how to handle the President.

Plus - what do Trump's latest comments mean for the Chagos deal? And why did the President seem so "exhausted"?

Could AI really 'kill us all' by the end of the decade?

That was the claim of a resigning researcher at AI giant Anthropic, which has caught the world's attention.

Jacob Coxon said Anthropic, the company behind AI assistant Claude, was "racing straight to self-improving superintelligence" and "gambling" with the lives of humanity as a result.

So are the explosive claims and others like it genuine or just a hyperbolic marketing strategy?

On Talking Politics, Tom Bradby and Robert Peston discuss that and what power the UK government has to force regulation on a global industry dominated by the US and China.

Having followed the technology's development and its political implications closely for many years, Robert also explains what the realistic threats are and why both the US and China have been reluctant to regulate until now.

Israel's Foreign Minister Gideon Sa'ar has announced counter sanctions following the UK government's decision to ban imports from illegal settlements in the West Bank.

On Talking Politics, Robert Peston and Daniel Hewitt discuss the timing of the decision, whether it has been driven by Labour Party politics and if it will actually help keep the possiblity of a two-state solution for Israel and Palestine alive.

The autumn Budget is looming, but rising borrowing costs could already be eating into Andy Burnham’s financial headroom. With the money available to deliver the 'radical' agenda he promised shrinking, the new PM and his Chancellor face tough choices: tax rises or spending cuts.

Can Burnham make those difficult choices and take on some of Labour’s most politically sensitive commitments, including the welfare bill and the pension triple lock, or will his tendency to ‘people please’ hold him back?

And with war in Iran continuing, driving up oil prices and impacting the health of the global economy, is Burnham’s biggest challenge the markets rather than his own MPs?

Tom Bradby and Robert Peston discuss on this week's Talking Politics.

Andy Burnham has only been prime minister for a little over two weeks - but has already made an impression with his very different style of leadership to Sir Keir Starmer and raft of policies relating to the cost of living, social care, and more.

He appears to have initially benefited from a bounce in the opinion polls, leading to some speculation about whether he will call an early general election.

But how much of his plans actually stand up to scrutiny - particularly his proposals for devolution? And is the 'Burnham bounce' real or, with unfavourable headlines on the prisoner early release scheme dominating this week, is the honeymoon period already over?

And does it give Reform UK and Nigel Farage the chance to bounce back?

Tom Bradby and Robert Peston discuss on this week's Talking Politics.

Andy Burnham has kicked off his 'cost of living' government with a flurry of announcements - starting with removing VAT from household energy bills and restoring the £2 cap on bus fares in England. But he has already rowed back on a potential rise in the tax-free personal allowance.

On Talking Politics, Tom Bradby and Robert Peston ask whether support is really being targeted towards those who most need it and whether it is ambitious enough to turn the country around. They also discuss his promise to end to factionalism, which coincided with a purge of the Starmerites.

Tom also asks Robert to explain exactly what 'war bonds' are and whether some creative government accounting could actually help solve the defence funding dilemma. Plus Robert analyses what the abolishment of the Department for Science, Innovation and Technology means for AI in the UK.

Andy Burnham is finally Prime Minister - so from bus fares to energy bills, what could it mean for you? Could a rise in the top rate of tax be on the cards, despite Labour's manifesto commitment?

On Talking Politics, Robert Peston and Tom Bradby discuss what he can to do to address the top priority of making life more affordable for people up and down the country.

Andy Burnham is just days from entering Number 10 - but what do we know about who will be in his top team?

In Talking Politics this week, Tom and Robert discuss who would be the best pick for Chancellor, and whether Ed Miliband’s Treasury dreams are over.

They break down what the handover of power will look like over the next few days, and how it could be impacted by the World Cup…

Tom and Robert also finish by reflecting on what the shocking murder of Ann Widdecombe could mean for British politics.

Nigel Farage has sent shockwaves through Westminster as he announced he would stand down as an MP but then contest the seat at the by-election.

Is it all a stunt to distract from scrutiny over his financial support as opposition parties say?

On this weeks’ Talking Politics, Robert is joined by ITV News Political Correspondent Harry Horton to discuss what this means for Farage’s political future.

Labour say the saga is a ‘circus’, while the Tories accuse Farage of having a ‘hissy fit’.

Robert and Harry discuss whether Count Binface could finally make it to Parliament, and whether Farage will come out of all of this looking ‘silly’.

Andy Burnham is headed for Downing Street and could be Prime Minister in just three weeks. But can he really deliver his bold vision without putting up taxes?

In this episode of Talking Politics, Robert is joined by Harry Horton, fresh from Burnham's major speech in Manchester, to unpack his economic blueprint.

From the promise to build more council homes to bringing essential services like energy and water back under public control, they explore Burnham's big ideas, his plans for a "Number 10 of the North", and ask: how will he pay for it?

In the second half of the episode, Robert speaks to Carl Dinnen about another looming financial headache: Keir Starmer's Defence Investment Plan has exposed a £4.7 billion funding gap. If Burnham takes the keys to Number 10, how can he plug that hole while delivering his own ambitious programme for change?