In physics, the graviton is a hypothetical elementary particle, a boson to be exact, that mediates the force of gravity in the framework of quantum field theory. If it exists, the graviton must be massless (because the gravitational force has unlimited range) and must have a spin of 2 (because gravity is a second-rank tensor field).
Gravitons are postulated because of the great success of the quantum field theory (in particular, the Standard Model) at modeling the behavior of all other forces of nature with similar particles: electromagnetism with the photon, the strong interaction with the gluons, and the weak interaction with the W and Z bosons. In this framework, the gravitational interaction is mediated by gravitons, instead of being described in terms of curved spacetime as in general relativity. In the classical limit, both approaches give identical results, which are required to conform to Newton's law of gravitation.
However, attempts to extend the Standard Model with gravitons run into serious theoretical difficulties at high energies (processes with energies close to or above the Planck scale) because of infinities arising due to quantum effects (in technical terms, gravitation is nonrenormalizable.) Some proposed theories of quantum gravity (in particular, string theory) address this issue. In string theory, gravitons (as well as the other particles) are states of strings rather than point particles, and then the infinities do not appear, while the low-energy behavior can still be approximated by a quantum field theory of point particles. In that case, the description in terms of gravitons serves as a low-energy effective theory.
String theory predicts the existence of gravitons and their well-defined interactions which represents one of its most important triumphs. A graviton in perturbative string theory is a closed string in a very particular low-energy vibrational state. The scattering of gravitons in string theory can also be computed from the correlation functions in conformal field theory, as dictated by the AdS/CFT correspondence, or from Matrix theory.
An interesting feature of gravitons in string theory is that, as closed strings without endpoints, they would not be bound to branes and could move freely between them. If we live on a brane (as hypothesized by some theorists) this "leakage" of gravitons from the brane into higher-dimensional space could explain why gravity is such a weak force, and gravitons from other branes adjacent to our own could provide a potential explanation for dark matter. See brane cosmology for more details.
However, experiments to detect gravitational waves, which may be viewed as coherent states of many gravitons, are already underway (e.g. LIGO and VIRGO). Although these experiments cannot detect individual gravitons, they might provide information about certain properties of the graviton. For example, if gravitational waves were observed to propagate slower than c (the speed of light in a vacuum), that would imply that the graviton has mass.