One of the hardest is still “What is light?”, a question that has puzzled philosophers for centuries, millennia even. We’ve gotten better at describing the phenomena associated with light, but if you keep drilling down, like a little kid asking “But why?”, you will get to possibly the biggest mystery in science.
Sure, we have theories – “a photon is a probability wave function” being a popular one. But, what actually is it? That really just describes the behaviour – the phenomena. What is actually happening, at a fundamental level?
Neils Bohr’s Copenhagen Interpretation (source of the above probability wave functions) kind of says “Hey, it’s pointless to try to discuss the underlying physics, all we can do is describe the behaviour”. Einstein thought this was a massive cop-out, and I agree with him.
String theory was an attempt to answer this question properly, but it seems to have tied itself up in knots, no pun intended, with all of the untestable predictions and required extra invisible dimensions. So, we still don’t know.