Humans have explored other planets and looked at distant galaxies, but we still know very little about the planet under our feet. Most of what we know about the Earth's structure and composition is based on the study of how earthquake waves are refracted as they pass through the planet's interior. The fact that it's made of rock and iron does make it hard to have a look at the inside.
Until now, direct study of the Earth's interior has been limited to the crust, but a pair of geologists have proposed drilling down to the Mohorovicic Discontinuity, which marks the boundary between crust and mantle. They wrote about it in Nature, but since that's hidden behind a subscription wall, you can read a news article about it instead.
If it works, let's hope it doesn't produce the same effect as this earlier attempt.
The actual drilling would pass through five or six kilometers of crust, but would have to be done at a place where the crust is thinnest -- a deep ocean trench where nature has already done most of the work. The deepest artificial hole is in Russia, at the Kola Superdeep Borehole. They went down twelve kilometers, but since the operation was on land, it only got part of the way through the crust (and not into Hell, as reported). Drilling at sea means less rock, but the operation is limited by the size of the available drill ships. The hope is that the research ship Chikyu can handle the job.