After another extraordinary week, we try to make sense of what Trump has been up to on his European travels. From Chequers to Brussels to Helsinki, what was he doing and why was he doing it? Is he really Putin's puppet? Has he helped or hurt May's chances of survival? Plus we catch up with the other side of the Trump presidency: the remaking of the US Supreme Court. How will the nomination of Brett Kavanaugh impact on some of the most contentious issues in American politics, above all the deep divisive question of abortion? With Helen Thompson and Gary Gerstle, Mellon Professor of American History at Cambridge.

With more Brexit chaos on us, we cut through some of the noise to talk about a new report on the future of referendums. How can we run them better in future? When is it appropriate to have a second referendum? What else can we do to reconnect democratic politics with the voters? With Gisela Stuart, former Labour MP and Chair of Vote Leave; Jenny Watson, former Chair of the Electoral Commission; and Alan Renwick of the Constitution Unit at UCL. Plus at the end some thoughts from David on where we are now. You can read the full report here: http://www.ucl.ac.uk/constitution-unit/research/electionsandreferendums/icreferendums

As the World Cup approaches its climax we talk politics and football, on the morning after England's dramatic penalty shootout win over Colombia. What happened to the warnings that this World Cup would be like the 1936 Berlin Olympics? Can we learn anything about German politics from the failure of the German football team? What does England's progress mean for Brexit? Plus much more, from Saudi Arabia to Croatia to West Ham. With Helen Thompson and Mike Kenny.

In a special live edition recorded at the Guardian's King's Place Politics Festival on Sunday 24th June - David, Helen and Chris Bickerton discuss whether the migration crisis has opened up a new dividing line in European politics. Is Viktor Orban right that Europe is now split between the countries that will accept immigrants and the countries that won't? What does that mean for Merkel's survival prospects? Where does Macron stand in this fight? Plus we take questions from the audience about what populism really means and what, if anything, we can do about the current state of politics.

David talks to Andrew O'Hagan about his epic essay in the LRB on the causes, consequences and fall-out of the terrible Grenfell Tower fire that happened a year ago. We discuss what the Grenfell community was like before the fire, what went wrong on the night, and how politics has intruded into everything that has happened since. Plus we talk about the angry push-back to Andrew's account. It can all be read here: https://www.lrb.co.uk/v40/n11/andrew-ohagan/the-tower

From the G7 to the Singapore summit, it's Trump's world: we just live in it. This week we try to get some perspective on these spectacular events. Is Trump's behaviour really unprecedented for an American president? What is the point of the G7? Where is his relationship with Kim heading? Plus we compare with summits past: Nixon in China, Reagan & Gorbachev, or something new? With Helen Thompson and Andrew Preston, who gives a Canadian view. Next week: Grenfell.

A new Italian government spells a heap of trouble for Europe. We ask how we got to this point and what it means the future of the Euro. What really spooked the markets? Who blinked first? And why does Italian politics have such a soft spot for university professors? Plus we talk about the new government in Spain and we weigh up the state of democracy across the continent. Is this how democracy is meant to work or is this really how democracy ends? With Helen Thompson, Chris Bickerton and Lucia Rubinelli from the LSE.

Chris Bickerton, a political science expert, and Chris Brooke, a specialist in socialist thought, dive into the meaning of socialism in today's political landscape. They explore whether socialism necessitates the downfall of capitalism and distinguish it from communism. The duo discusses socialism's appeal in the U.S., especially amidst rising democratic candidates adopting the label. They also contemplate if social media can inspire a modern form of socialism, considering young voters' changing perceptions and influences in both America and Britain.

This week we try to make sense of what's happening to the international order, from the end of the Iran deal to the on-again-off-again US-North Korean summit to opening of the US embassy in Jerusalem. Can Europe carve out a separate foreign policy from the Trump administration? Is regime change still the name of the game? And what has it all got to do with the price of oil? Plus we ask if anything is left of Obama's legacy and why it was so easy to undo. With Helen Thompson, Aaron Rapport and Chris Bickerton. 

This week we discuss how and why mental health has become a growing political issue. What are the differences in the way the political parties approach this problem? Is it something that unites or divides people across generations and classes? And what can politicians do to help us cope? Plus we talk about whether politics itself has become a more stressful job than it used to be. With Helen Thompson and Chris Brooke.