The QuantumFrontiers consortium comprises experts in general relativity and its test on macroscopic scales using *Lunar Laser Ranging**, *which succeeded inlimiting a possible *temporal drift of the gravitational constant*to a world record of Ġ/G~1 x 10^{-13}1/yr and verified the strong equivalence principle to η~3 x 10^{-4}. Furthermore, QuantumFrontiers researchers have used their clocks to obtain the most stringent limits so far for a possible temporal variation of dimensionless fundamental constants, like the fine-structure constant and the electron-proton mass ratio, which are predicted to change their value e.g. through coupling to dark matter. Within QuantumFrontiers, we will improve optical clock performance and make sensitive systems available through quantum logic spectroscopy, to further reduce these limits by more than one order of magnitude and thus contribute to excluding dark matter candidates and to a test of CPT symmetry violation. Furthermore, we will perform classical and quantum tests of relativity by probing Newton’s axioms, performing improved local Lorentz-invariance, redshift and universality of free-fall tests, and by investigating possible fundamental sources of decoherence in strongly delocalised quantum objects.