General relativity does describe the nature of spacetime and the resulting gravitational effects quite well, though you have to keep in mind that any theory (except by definition a fundamental theory from which all else follows) has its regime of applicability, beyond which it will give nonsense results.
Take as the prototype: Newtonian vs. Qauntum mechanics. QM is supposed to be the more fundamental theory, which it is, from which Newtonian physics should arise, which it does. No one would doubt (except cranks perhaps) that Newtonian physics works fine for everyday "human" scales...and even though QM is supposed to be more fundamental theory, this doesn't mean we go out and apply it to describe planes in flight. The reasons: (1) Describing the system in terms of the consituents is too complicated...also, talking about the protons, neutrons, and electrons making up the plane and surrounding air in motion is not very useful to describe the macroscopic object. (2) Newtonian mechanics is a very good approximation when talking about a collective object like a plane, so using QM and talking about all the particles making up the plane would be overkill in accuracy anyway.
The same discussion applies to general relativity, where this now plays the role of the effective theory describing macroscopic scales quite nicely. However, the theory does not apply below a certain distance scale: for example, it can't handle extreme spacetime curvatures well (singularities are the signal here). Therefore, it is commonly believed in the physics community that there is a more fundamental theory describing the nature of spacetime, and that general relativity should emerge from it at the distance scales where it is a good approximation. In addition, spacetime is dynamical, and we would expect quantum mechanics to apply to it as well...why should only electrons, light, and everything else *other than* spacetime behave fundamentally qauntum mechanically?
Gravitons arise as a description that tries to mirror what was done for *all the other known constituents of the universe*: by using quantum field theory. The idea here is that gravitons arise as quantum excitations of spacetime, but in a way that is still an approximation: we consider only fluctuations of spacetime about a given background spacetime that is smooth down to the smallest distance scales. There are arguments that the reason this description doesn't work as a truly fundamental theory of spacetime is that spacetime structure is *not smooth* down to all distance scales...that the geometry of spacetime is quantized...it, too, has fundamental constituents!
Some physicists work on such an attempt at quantizing spacetime starting with the classic general relativistic theory. Gravitons would arise as a more macroscopic (albeit a tiny macroscopic) approximation to what's really going on. This approach is called "Qauntum Geometry" to distinguish it from any other qauntum gravity theories.
A larger group of physicists work in string theory, which is any possible way to find a fundamental theory of spacetime (and with it, everything else tied together!). More ambitious, no? This is the camp that gets more attention...like Nova specials and magazine articles.
In the end, one must be careful to remember that neither of these paths (quantum geometry and string theory) have any testable predictions yet, and so they are hypotheses for the way things are...so talking about gravitons and strings as if they are known to exist is misleading. The Standard Model of particle physics, on the other hand, has been (and continues to be) tested and though it is still not the most fundamental description of things, it is a beautiful thing.
On that note, good night.
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