Humans have been all over the Earth. We've conquered the lands, flown through the air and dived to the deepest trenches in the ocean. We've even been to the Moon. But we've never been to the planet's core.

We haven't even come close. The central point of the Earth is over 6,000km down, and even the outermost part of the core is nearly 3,000 km below our feet. The deepest hole we've ever created on the surface is the Kola Superdeep Borehole in Russia, and it only goes down a pitiful 12.3 km.

All the familiar events on Earth also happen close to the surface. The lava that spews from volcanoes first melts just a few hundred kilometres down. Even diamonds, which need extreme heat and pressure to form, originate in rocks less than 500km deep.

What's down below all that is shrouded in mystery. It seems unfathomable. And yet, we know a surprising amount about the core. We even have some idea about how it formed billions of years ago – all without a single physical sample. This is how the core was revealed.

One good way to start is to think about the mass of the Earth, says Simon Redfern of the University of Cambridge in the UK.

Most of the Earth's mass must be located towards the centre of the planet

We can estimate Earth's mass by observing the effect of the planet's gravity on objects at the surface. It turns out that the mass of the Earth is 5.9 sextillion tonnes: that's 59 followed by 20 zeroes.

There's no sign of anything that massive at the surface.

"The density of the material at the Earth's surface is much lower than the average density of the whole Earth, so that tells us there's something much denser," says Redfern. "That's the first thing."

Essentially, most of the Earth's mass must be located towards the centre of the planet. The next step is to ask which heavy materials make up the core.

The answer here is that it's almost certainly made mostly of iron. The core is thought to be around 80% iron, though the exact figure is up for debate.

An iron core would account for all that missing mass

The main evidence for this is the huge amount of iron in the universe around us. It is one of the ten most common elements in our galaxy, and is frequently found in meteorites.

Given how much there is of it, iron is much less common at the surface of the Earth than we might expect. So the theory is that when Earth formed 4.5 billion years ago, a lot of iron worked its way down to the core.

That's where most of the mass is, and it's where most of the iron must be too. Iron is a relatively dense element under normal conditions, and under the extreme pressure at the Earth's core it would be crushed to an even higher density, so an iron core would account for all that missing mass.

But wait a minute. How did that iron get down there in the first place?

The iron must have somehow gravitated – literally – towards the centre of the Earth. But it's not immediately obvious how.

Most of the rest of the Earth is made up of rocks called silicates, and molten iron struggles to travel through them. Rather like how water on a greasy surface forms droplets, the iron clings to itself in little reservoirs, refusing to spread out and flow.

The pressure actually changes the properties of how iron interacts with the silicate

A possible solution was discovered in 2013 by Wendy Mao of Stanford University in California and her colleagues. They wondered what happened when the iron and silicate were both exposed to extreme pressure, as happens deep in the earth.

By pinching both substances extremely tightly using diamonds, they were able to force molten iron through silicate.

"The pressure actually changes the properties of how iron interacts with the silicate," says Mao. "At higher pressures a 'melt network' is formed."

This suggests the iron was gradually squeezed down through the rocks of the Earth over millions of years, until it reached the core.

At this point you might be wondering how we know the size of the core. What makes scientists think it begins 3000km down? There's a one-word answer: seismology.

All the seismic stations dotted all over the Earth recorded the arrival of the tremors

When an earthquake happens, it sends shockwaves throughout the planet. Seismologists record these vibrations. It's as if we hit one side of the planet with a gigantic hammer, and listened on the other side for the noise.

"There was a Chilean earthquake in the 1960s that generated a huge amount of data," says Redfern. "All the seismic stations dotted all over the Earth recorded the arrival of the tremors from that earthquake."

Depending on the route those vibrations take, they pass through different bits of the Earth, and this affects how they "sound" at the other end.

Early in the history of seismology, it was realised that some vibrations were going missing. These "S-waves" were expected to show up on one side of the Earth after originating on the other, but there was no sign of them.

It turned out that rocks became liquid around 3000km down

The reason for this was simple. S-waves can only reverberate through solid material, and can't make it through liquid.

They must have come up against something molten in the centre of the Earth. By mapping the S-waves' paths, it turned out that rocks became liquid around 3000km down.

That suggested the entire core was molten. But seismology had another surprise in store.

In the 1930s, a Danish seismologist named Inge Lehmann noticed that another kind of waves, called P-waves, unexpectedly travelled through the core and could be detected on the other side of the planet.

P-waves really were travelling through the core

She came up with a surprising explanation: the core is divided into two layers. The "inner" core, which begins around 5,000km down, was actually solid. It was only the "outer" core above it that was molten.

Lehmann's idea was eventually confirmed in 1970, when more sensitive seismographs found that P-waves really were travelling through the core and, in some cases, being deflected off it at angles. Sure enough, they still ended up on the other side of the planet.

It's not just earthquakes that sent useful shockwaves through the Earth. In fact, seismology owes a lot of its success to the development of nuclear weapons.

A nuclear detonation also creates waves in the ground, so nations use seismology to listen out for weapons tests. During the Cold War this was seen as hugely important, so seismologists like Lehmann got a lot of encouragement.

This turns out to be quite tricky to determine

Rival countries found out about each other's nuclear capabilities and along the way we learned more and more about the core of the Earth. Seismology is still used to detect nuclear detonations today.

We can now draw a rough picture of the Earth's structure. There is a molten outer core, which begins roughly halfway to the planet's centre, and within it is the solid inner core with a diameter of 1,220 km.

But there is a lot more to try and tease out, especially about the inner core. For starters, how hot is it?

This turns out to be quite tricky to determine, and baffled scientists until quite recently, says Lidunka Vočadlo of University College London in the UK. We can't put a thermometer down there, so the only solution is to create the correct crushing pressure in the lab.

Earth's core has stayed warm thanks to heat retained from the formation of the planet

In 2013 a team of French researchers produced the best estimate to date. They subjected pure iron to pressures a little over half that at the core, and extrapolated from there. They concluded that the melting point of pure iron at core temperatures is around 6,230 °C. The presence of other materials would bring the core's melting point down a bit, to around 6,000 °C. But that's still as hot as the surface of the Sun.

A bit like a toasty jacket potato, Earth's core has stayed warm thanks to heat retained from the formation of the planet. It also gets heat from friction as denser materials shift around, as well as from the decay of radioactive elements. Still, it is cooling by about 100 °C every billion years.

Knowing the temperature is useful, because it affects the speed at which vibrations travel through the core. That is handy, because there is something odd about the vibrations.

P-waves travel unexpectedly slowly as they go through the inner core – slower than they would if it was made of pure iron.

It's a Cinderella problem: no shoe will quite fit

"Wave velocities that the seismologists measure in earthquakes and whatnot are significantly lower [than] anything that we measure in an experiment or calculate on a computer," says Vočadlo. "Nobody as yet knows why that is."

That suggests there is another material in the mix.

It could well be another metal, called nickel. But scientists have estimated how seismic waves would travel through an iron-nickel alloy, and it doesn't quite fit the readings either.

Vočadlo and her colleagues are now considering whether there might be other elements down there too, like sulphur and silicon. So far, no-one has been able to come up with a theory for the inner core's composition that satisfies everyone. It's a Cinderella problem: no shoe will quite fit.

That could explain why the seismic waves pass through more slowly than expected

Vočadlo is trying to simulate the materials of the inner core on a computer. She hopes to find a combination of materials, temperatures and pressures that would slow down the seismic waves by the right amount.

She says the secret might lie in the fact that the inner core is nearly at its melting point. As a result, the precise properties of the materials might be different from what they would be if they were safely solid.

That could explain why the seismic waves pass through more slowly than expected.

"If that's the real effect, we would be able to reconcile the mineral physics results with the seismological results," says Vocadlo. "People have not been able to do that yet."

There are plenty of riddles about the earth's core still to solve. But without ever digging to those impossible depths, scientists have figured out a great deal about what is happening thousands of kilometres beneath us.

The magnetic field helps to shield us from harmful solar radiation

Those hidden processes in the depths of the Earth are crucial to our daily lives, in a way many of us don't realise.

Earth has a powerful magnetic field, and that is all thanks to the partially molten core. The constant movement of molten iron creates an electrical current inside the planet, and that in turn generates a magnetic field that reaches far out into space.

The magnetic field helps to shield us from harmful solar radiation. If the core of the Earth wasn't the way it is, there would be no magnetic field, and we would have all sorts of problems to contend with.

None of us will ever set eyes on the core, but it's good to know it's there.