Albert Einstein pointed out, in 1907 and 1911, that his principle of equivalence would lead to the shift of stellar spectral lines to the red when produced in more massive sources than the Earth. This became one of the `three crucial tests' of his 1917 general theory of relativity. Astronomers searched for it for several decades with rather inconclusive results. A new approach was created by the discovery of recoil-free emission and the absorption of gamma-rays, with widths basically determined by nuclear state lifetimes, announced in 1958 by Rudolph Mössbauer. Glen Rebka and I were quickly able to extend that new technique to the example of 57Fe and to demonstrate the miniscule shift within a 23 m tower in the laboratory. By 1964, with J L Snider, I was able to reduce the uncertainty to less than 1% of the 2.5×10-15 fractional effect predicted. In 1977 a long anticipated combination of atomic clocks and space vehicles by R F C Vessot and NASA confirmed the effect in its time-keeping aspect to better than one part in 10 000.