This interesting cube-diagram is from Jess Riedels' blog.
The idea of this diagram is that the fundamental theories of physics can be placed in three dimensions as to how they treat gravity, the speed of light and Planck's constant h-bar, ℏ.
G is Newton's gravitational constant as in his law F = Gm1m2/r2. When we dial G to zero we're in domains where we ignore the effects of gravity. Most of quantum theory is here, as is special relativity and classical mechanics.
The speed of light
Strictly speaking the important thing about our universe is not the weirdness of the speed of light, it's that in the large the universe's structure is Minkowski spacetime, not our intuitive 3D Euclidean space + time. This is a difference in metric, as well-explained here.
If you dial the speed of light to infinity (so 1/c goes to zero) then the space + time metric tends to that of common sense.
This is the weird one. Quantum phenomena such as superposition and entanglement emerge mathematically from the non-zero value of ℏ, most clearly seen in the uncertainty principle.
However, the emergence of classical physics from quantum mechanics as you reduce ℏ to zero isn't too clear. The state space of quantum mechanics is an abstract structure, a complex high-dimensional vector space called Hilbert space, which is not directly mappable to spacetime.
You might say that seven out of the eight nodes on this cube are well-established - the central mystery of contemporary fundamental physics is the eighth, quantum gravity.