Binary stars are foundation stones for modern astrophysics: they give rise to key phenomena that we study at all energies and redshifts; also, they are precision clockworks for deriving fundamental parameters for Stellar Evolution and Galactic Archaeology; and their orbital characteristics still carry the imprints of the formation process and of later dynamical interactions. The GAIA satellite mission has provided the ultimate sample for studying binaries, providing millions of astrometric orbits. However, for the vast majority GAIA is not able to spatially resolve the components, but measures only the motion of the photocenter between the stars. This prevents GAIA from deriving dynamical masses and strongly limits what we can learn about star and planet formation. In the project we build on the GAIA sample to study the dynamical processes that shape system architectures, over the whole mass range from stellar-mass companions down to planets. This will reveal what mechanisms are common between binary formation and planet formation, and how they differ. To achieve this goal, we build a 4-telescope instrument for the Very Large Telescope Interferometer, called BIFROST. With each single pointing, BIFROST will turn a GAIA binary into a fully-characterised system, with 3-dimensional orbits, precision dynamical masses and precision ages. Also, BIFROST will be the only VLTI instrument optimised for high spectral resolution. This allows us to measure the alignment between the stellar spin axis and the orbital axis for wide-separation systems that are inaccessible with other techniques, providing a key diagnostic on their dynamical history. Third, we image young stars with discs that show evidence for companion-disc interactions. We conduct deep multi-wavelength, multi-epoch imaging and model the observed disc structures to better understand the hydrodynamical effects that shape discs. The BIFROST survey will explore the origin of the diversity that we see in binary and planetary systems. It will provide the largest ever sample of precision dynamical masses and ages, which will have a tremendous impact in Stellar Evolution and Galactic Archaeology. Finally, BIFROST will break new ground for VLTI, leading the way for short-wavelength characterisation of exoplanet atmospheres in the future.