"Why do we dream and why do we repeat dreams?" asks Mila O'Dea, aged 9, from Panama.

Hannah and Adam delve into the science of sleep. From a pioneering experiment on rapid eye movement sleep, to a brand new 'dream signature' found in the brain, they discover how scientists are investigating our hidden dreamworld.

Featuring sociologist Bill Domhoff from the University of California Santa Cruz, sleep psychologist Mark Blagrove from the University of Swansea, and neurologist Francesca Siclari from the University of Lausanne.

Presenters: Adam Rutherford, Hannah Fry

Why do we get static shocks?

Jose Chavez Mendez from Guatemala asks, "Some years ago, in the dry season, I used to be very susceptible to static electricity. I want to know - why do static shocks happen?"

The team uncover some slightly unethical science experiments on static electricity from the 1700s. Hannah Fry uses a Leyden Jar to demonstrate how static electricity works with help from her glamorous assistant, Adam Rutherford. Spoiler Alert: it doesn't end well for Adam.

They discover what makes some people more susceptible to static shocks, and how bees and spiders have harnessed the awesome power of electricity.

Featuring electromagnetism scientist Rhys Phillips and physicist Helen Czerski, author of 'Storm in a Teacup: The Physics of Everyday Life'.

Presenters: Adam Rutherford, Hannah Fry

Why do songs get stuck in our heads? And what makes some tunes stickier than others?

Drs Rutherford and Fry investigate 'earworms', those musical refrains that infect our brains for days. Every morning 6Music DJ Shaun Keaveney asks his listeners for their earworms, and Hannah finds out which tunes keep coming back.

Adam asks Dr Lauren Stewart, from Goldsmiths University, to reveal the musical features that make some songs catchier than others.

And they find out why, in times of crisis, an earworm may just save your life.

Producer: Michelle Martin.

No one knows why the Earth's magnetic North and South poles swap. But polar reversals have happened hundreds of times over the history of the Earth.

So, asks John Turk, when is the next pole swap due and what will happen to us?

Hannah turns to astronomer Lucie Green from Mullard Space Science Laboratory to discover how the earth's magnetic field protects us from the ravages of space. And Adam consults geophysicist Phil Livermore from the University of Leeds to find out if, and when, we're facing a global apocalypse.

Plus astronaut Terry Virts, author of The View from Above, describes his experiences of a strange magnetic glitch in the earth's magnetic field, known as The Bermuda Triangle of Space, which could help us prepare for the next event.

Presenters: Hannah Fry, Adam Rutherford

Can chemistry help us bake the perfect cake?

Listener Helena McGinty aged 69 from Malaga in Spain asks, "'I have always used my mother's sponge cake recipe. But is there a noticeable difference in the outcome if you vary some of the ingredients, or the method?"

In this episode Hannah and Adam go head to head in a competition to create the perfect cake using the power of science.

They are aided by materials scientist Mark Miodownik, from University College London, with tips on how to combine the ideal ingredients and trusted techniques to construct a structurally sound sponge.

Jay Rayner, food critic and presenter of Radio 4's The Kitchen Cabinet, is on hand to judge the results. But who will emerge victorious in this messy baking battle?

Presenters: Hannah Fry, Adam Rutherford

"It started while listening to the excellent Experiment IV by Kate Bush. The premise of the song is of a band who secretly work for the military to create a 'sound that could kill someone'. Is it scientifically possible to do this?" asks Paul Goodfield.

Hannah consults acoustic engineer Trevor Cox to ask if sonic weapons could kill. And Adam delves into subsonic frequencies with parapsychologist Chris French to investigate their spooky effects.

You can send your everyday mysteries for the team to investigate to: [email protected]

Presenters: Adam Rutherford, Hannah Fry

"What is an itch and how does scratching stop it? Why does scratching some itches feel so good?!" asks Xander Tarver from Wisborough Green in West Sussex.

Our doctors set off to probe the mysteries of itch, and discover that this overlooked area of medicine is revealing surprising results about the human brain. From why itching is contagious to why scratching is pleasurable, we get under the skin of this medical mystery.

The programme features interviews with neuroscientist Prof Francis McGlone from Liverpool John Moores University, and dermatologist Dr Brian Kim from the Center for the Study of Itch at Washington University. Yes, that is a real place.

You can send your everyday mysteries for the team to investigate to: [email protected]

Presenters: Adam Rutherford, Hannah Fry

"What is fire? Is it a solid, liquid or a gas? Why is it hot and why can you see it in the dark?" asks Hannah Norton, aged 10.

Dr Fry visits the Burn Hall at The Buildings Research Establishment in Watford where they test the effects of fire on building materials.

Whilst Dr Rutherford gets to grips with Michael Faraday's pioneering Christmas Lectures at the Royal Institution of Great Britain on 'The Chemical History of a Candle'. Plus, he chats to forensic chemist Niamh Nic Daeid from Dundee University about our lasting fascination with fire.

You can send your Curious Cases for the team to investigate to: [email protected]

Presenters: Hannah Fry, Adam Rutherford

"What's inside a black hole and could we fly a spaceship inside?" asks Jorge Luis Alvarez from Mexico City.

Some interstellar fieldwork is on the agenda in today's Curious Cases. Astrophysicist Sheila Rowan explains how we know invisible black holes actually exist. And cosmologist Andrew Pontzen is on hand to help cook one up.

But which of our intrepid doctors will volunteer to fly into the heart of a black hole?

You can send your Curious Cases for the team to investigate to: [email protected]

Presenters: Hannah Fry, Adam Rutherford

"How on earth do cats find their way back to their previous home when they move house?" asks Vicky Cole from Nairobi in Kenya.

Our enduring love for our feline friends began when Egyptian pharaohs began to welcome domesticated moggies into their homes. Pictured reclining in baskets at the feet of royalty, pet cats soon became fashionable throughout society in Egypt.

Today they are the most popular pet in the world, and home is definitely where their hearts lie.

"Whereas dogs are bonded to people, cats are bonded to place," explains zoologist Dr John Bradshaw. "It's very typical for them to try and find their way back to their old house when you move."

But how do they do it? And if their navigational skills are so good, why do they get lost?

Plus, Prof Matthew Cobb reveals the super-senses that cats possess, which humans don't, and how to spot when your cat is deploying them.

You can send your Curious Cases for the team to investigate to: [email protected]

Presenters: Hannah Fry, Adam Rutherford