Review of recent works devoted to the variation of the fine structure constant α, strong interaction and fundamental masses (Higgs vacuum) is presented. The results from Big Bang nucleosynthesis, quasar absorption spectra, and Oklo natural nuclear reactor data give us the space-time variation on the Universe lifetime scale. Comparison of different atomic clocks gives us the present time variation. Assuming linear variation with time we can compare different results. The best limit on the variation of the electron-to-proton mass ratio μ = me/Mp and Xe = me/ΛQCD follows from the quasar absorption spectra:1[Formula: see text]. A combination of this result and the atomic clock results2,3 gives the best limt on variation of [Formula: see text]. The Oklo natural reactor gives the best limit on the variation of Xs = ms/ΛQCD where ms is the strange quark mass:4,5[Formula: see text]. Note that the Oklo data can not give us any limit on the variation of α since the effect of α there is much smaller than the effect of Xs and should be neglected. Huge enhancement of the relative variation effects happens in transitions between close atomic, molecular and nuclear energy levels. We suggest several new cases where the levels are very narrow. Large enhancement of the variation effects is also possible in cold atomic and molecular collisions near Feshbach resonance. How changing physical constants and violation of local position invariance may occur? Light scalar fields very naturally appear in modern cosmological models, affecting parameters of the Standard Model (e.g. α). Cosmological variations of these scalar fields should occur because of drastic changes of matter composition in Universe: the latest such event is rather recent (about 5 billion years ago), from matter to dark energy domination. Massive bodies (stars or galaxies) can also affect physical constants. They have large scalar charge S proportional to number of particles which produces a Coulomb-like scalar field U = S/r. This leads to a variation of the fundamental constants proportional to the gravitational potential, e.g. δα/α = kαδ(GM/rc2). We compare different manifestations of this effect. The strongest limits6kα + 0.17ke = (-3.5 ±6) × 10-7 and kα + 0.13kq = (-1 ± 17) × 10-7 are obtained from the measurements of dependence of atomic frequencies on the distance from Sun2,7 (the distance varies due to the ellipticity of the Earth's orbit).
LET'S TALK ABOUT VARYING G