  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+.
