We present evidence for variations in the fine-structure constant from Keck/HIRES spectra of 143 quasar absorption systems over the redshift range 0.2 < z_abs < 4.2. This includes 15 new systems, mostly at high-z (z_abs > 1.8). Our most robust estimate is a weighted mean da/a=(-0.57 +/- 0.11)x10^{-5}. We respond to recent criticisms of the many-multiplet method used to extract these constraints. The most important potential systematic error at low-z is the possibility of very different Mg heavy isotope abundances in the absorption clouds and laboratory: {it higher} abundances of {25,26}Mg in the absorbers may explain the low-z results. Approximately equal mixes of {24}Mg and {25,26}Mg are required. Observations of Galactic stars generally show {it lower} {25,26}Mg isotope fractions at the low metallicities typifying the absorbers. Higher values can be achieved with an enhanced population of intermediate mass stars at high redshift, a possibility at odds with observed absorption system element abundances. At present, all observational evidence is consistent with the varying-alpha results. Another promising method to search for variation of fundamental constants involves comparing different atomic clocks. Here we calculate the dependence of nuclear magnetic moments on quark masses and obtain limits on the variation of alpha and m_q/Lambda_QCD from recent atomic clock experiments with hyperfine transitions in H, Rb, Cs, Hg+ and an optical transition in Hg+.
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