Doctor Who

7.25pm Saturday, BBC1

The Doctor, wearing sonic sunglasses and standing in an empty lecture hall, is mystified by a personal visit from the Pope. “Why would you do that?” he enquires, not altogether respectfully. It turns out a new translation has been posted online of an ancient document called Veritas contained in a secret Vatican library. The problem? Those who have read it have all taken their own lives. Can the Doctor solve the riddle – and survive?

An elegant pre-credits feint sets the tone for a typically classy mind-bender from outgoing showrunner Steven Moffat. As you’d expect, it doesn’t neglect the funny (a papal audience for Bill plus ever-fretful Nardole). Otherwise this is a dark and rich existential workout, taking The Ring, The Name of the Rose and The Matrix as its reference points, and even the reintroduced Missy the minx (Michelle Gomez) is in subdued mood. And this may just be me, but at times I thought there was a slight Bond vibe going on. 

Flitting between Rome, Cern, Washington and a far-off world, Extremis shows a writer in calm control of his material, and Peter Capaldi in private agonies as the careworn Doctor.

Hinterland

9pm Saturday, BBC4

The sun peeps from behind the clouds to baste Aberystwyth in a rosy glow. But it doesn’t last. The mist rolls up on to the hills as a man is blasted to death with a sawn-off shotgun at a petrol station. 

It’s the start of an arduous, dangerous murder hunt for DCI Tom Mathias, still warm from his comely landlady’s duvet, and his tiny team of detectives. There’s no whodunnit element – we quickly learn the identity of the murderer; it’s all about motivation and the police search for their quarry.

We know that Mathias (Richard Harrington) likes to act alone, so when he disappears to track down the murderer – a Phil Collins look-alike who’s taken his young son from school – his colleagues are left to fret about his fate. 

It’s an absorbing tale that owes something to Truman Capote’s In Cold Blood, with a few gothic twists.

Philomena

9pm Saturday, BBC2

Judi Dench is on sparkling form as the titular Irish woman whose child was snatched away by nuns at a time when giving birth out of wedlock was treated as a criminal act. Decades later, journalist Martin Sixsmith represents her only hope of finding her son (the film is based on his 2009 book The Lost Child of Philomena Lee). Steve Coogan is suitably irascible as the former BBC correspondent, just publicly fired from his second career as a Labour government adviser, initially turning his nose up at the idea of pursuing a "human interest story".

But Philomena, brimming with religious faith and optimism, is such a force of nature that he can't help but be swayed. Director Stephen Frears exploits the odd-couple dynamic to great effect, not only generating wonderful comic moments but also bringing home the tragedy of Philomena's life. He might have given their journey to America a little more cinematic sweep, but it's no less inspiring for that. You'll laugh and you'll cry, sometimes both at the same time. USED 20/05/2017 Based on the true story of how Philomena Lee (Judi Dench) spent 50 years seeking her long-lost illegitimate son. She was 17 when she gave birth in an Irish abbey. The nuns there sold her child to an American couple for £1,000.

Philomena's search becomes more urgent when former BBC correspondent Martin Sixsmith (Steve Coogan) hears of it and offers to help. They reach a dead end in Ireland when they learn that the nuns had conveniently burnt all records of the transaction so they go to America to look for the boy. This is at heart a horrifying tale which, thanks to the two stars and the Oscar-nominated screenplay by Coogan and Jeff Pope, is both very moving and funny. Dench is as immaculate as ever and Coogan is excellent in a straight, dramatic role. 

Inspector George Gently

8.30pm Sunday, BBC1

Honourable, decent DI George Gently. It looks like it’s all over. Coppering has moved on, it’s 1970 and the North East Constabulary faces major upheavals. “Change is always hard,” Gently’s patronising boss tells him. “We need a decision on your retirement.”

Gently (Martin Shaw) knows his time is up in the first of a brief (two-part), last-ever outing, which has Gently and his sidekick Bacchus’s futures very much at its heart.

Bacchus (Lee Ingleby, most recently seen as craven Nick Huntley in The Line of Duty) is a mess – seedy and drinking too much after the collapse of his marriage. One of his old cases looms when a man’s body is found in a chemical tank at a plant on Teesside. His wife has served eight years for his murder.

But Bacchus cut corners during the original investigation and, in an absorbing, sad tale, Gently knows that wrongs must be put right.

The Trial: A Murder in the Family

9pm Sunday, Channel 4

A university lecturer finds his estranged wife dead on the floor of the family home. She’s been strangled, but he takes an unconscionable amount of time to alert the emergency services. Eventually, he’s arrested and charged with her murder. 

This enthralling Channel 4 experiment, which runs nightly until a “verdict” is delivered on Thursday, does its best to look into the heart of the British jury system by presenting 12 randomly chosen men and women, ordinary members of the public, with a court case. But it’s a construct, the accused and the witnesses are actors, and the judge and the defence and prosecution teams are played by a retired judge and real barristers.

The Trial is extremely well put together and works just as much as an absorbing drama as an intriguing social experiment about perception and humanity.

The Keepers

Netflix

Sister Cathy Cesnik, a teacher at a Catholic high school in Baltimore, was murdered in 1969; the case remains unsolved. What appears to be merely a spooky whodunnit is soon revealed, in a gripping, troubling series, to be a tale not just of murder but of sexual abuse on a horrifying scale, involving the police and the church. The victims show extreme bravery by describing what happened, and its lasting effects.