I'm not sure what your threshold for "barely mentioned in the literature" is, since some of the highly-voted answers seem rather well known to me, but here's one that is certainly fundamental, seemingly out of reach, and perhaps not so well known except to complexity theorists.
Describe explicitly a Boolean function whose minimum circuit size is superlinear.
A simple counting argument shows that almost all Boolean functions require exponentially large circuits to express. However, giving explicit examples is another matter. Here, "explicit" is a bit vague, but let's say for example that it means that the truth table can be computed in time polynomial in the size of the truth table. Thus NP-complete Boolean functions count as "explicit," and proving superpolynomial circuit lower bounds for them would separate P from NP, but even if we weaken the requirement to a superlinear lower bound on any explicit function, nobody seems to have any clue.
