In many of the pop-science-y documentaries on theoretical physics I often hear the statement: "General Relativity and Quantum Mechanics are incompatible"

Some googling tells me that "General Relativity cannot be quantized" - my understanding of this statement is superficial.

What exactly does this mean?

I have taken quite a few courses on Quantum Mechanics, and am very comfortable with the subject. I have also taken a course in General Relativity, so I understand its formalism decently well.

Can someone explain this to me? If someone could provide me with some papers/links/literature on the subject I would also be very grateful.