GG Tau is a hierarchical quadruple system of young, low-mass stars. Because of its well-studied bright circumbinary ring of dust and gas surrounding the main binary GG Tau A, it is a unique laboratory to study planet formation in the disturbed environment of binary/multiple stellar systems. We have started a large observing program of GG Tau A that combines several high-resolution instruments in a multi-wavelength approach. We have recently reported the detection of a new low-mass companion in GG Tau A that turns out to itself be a triple system. This discovery was possible thanks to the very high angular resolution of the near-IR instrument PIONIER on the VLT interferometer, and was confirmed with sub-aperture masking techniques on VLT/NaCo. The detected close binary GG Tau Ab (ρ = 0.032'', or about 5 AU) provides a natural explanation for two enigmas: the discrepancy between the dynamical mass and the spectral type estimates in GG Tau A, and the absence of dust thermal emission in the vicinity of the Ab component. GRAVITY will provide the adequate angular resolution to complete the astrometric characterization of the close binary in the next 10 years. With now 5 coeval low-mass stars, GG Tau is an ideal laboratory to calibrate stellar evolution tracks at young ages (few Myr). Beyond this peculiar system, GRAVITY also has a strong potential to study the impact of multiplicity on the existence of disks, and in fine on planet formation mechanisms in multiple systems.