Review of recent works devoted to the variation of the fine structure constant \alpha , 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 \mu = m _ { e } / M _ { p } and X _ { e } = m _ { e } / \Lambda _ { QCD } follows from the quasar absorption spectra ( ( 1 ) ) : \dot { \mu } / \mu = \dot { X _ { e } } / X _ { e } = ( 1 \pm 3 ) \times 10 ^ { -16 } yr ^ { -1 } .
A combination of this result and the atomic clock results ( ( 2 ) ; ( 3 ) ) gives the best limt on variation of \alpha : \dot { \alpha } / \alpha = ( -0.8 \pm 0.8 ) \times 10 ^ { -16 } yr ^ { -1 } .
The Oklo natural reactor gives the best limit on the variation of X _ { s } = m _ { s } / \Lambda _ { QCD } where m _ { s } is the strange quark mass ( ( 4 ) ; ( 5 ) ) : | \dot { X _ { s } } / X _ { s } | < 10 ^ { -18 } yr ^ { -1 } .
Note that the Oklo data can not give us any limit on the variation of \alpha since the effect of \alpha there is much smaller than the effect of X _ { s } 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 . \alpha ) .
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 . \delta \alpha / \alpha = k _ { \alpha } \delta ( GM / rc ^ { 2 } ) .
We compare different manifestations of this effect .
The strongest limits ( ( 6 ) ) k _ { \alpha } +0.17 k _ { e } = ( -3.5 \pm 6 ) \times 10 ^ { -7 } and k _ { \alpha } +0.13 k _ { q } = ( -1 \pm 17 ) \times 10 ^ { -7 } are obtained from the measurements of dependence of atomic frequencies on the distance from Sun ( ( 2 ) ; ( 7 ) ) ( the distance varies due to the ellipticity of the Earth ’ s orbit ) .