  Efforts to place limits on deviations from canonical formulations of
electromagnetism and gravity have probed length scales increasing dramatically
over time.Historically, these studies have passed through three stages: (1)
Testing the power in the inverse-square laws of Newton and Coulomb, (2) Seeking
a nonzero value for the rest mass of photon or graviton, (3) Considering more
degrees of freedom, allowing mass while preserving explicit gauge or
general-coordinate invariance. Since our previous review the lower limit on the
photon Compton wavelength has improved by four orders of magnitude, to about
one astronomical unit, and rapid current progress in astronomy makes further
advance likely. For gravity there have been vigorous debates about even the
concept of graviton rest mass. Meanwhile there are striking observations of
astronomical motions that do not fit Einstein gravity with visible sources.
"Cold dark matter" (slow, invisible classical particles) fits well at large
scales. "Modified Newtonian dynamics" provides the best phenomenology at
galactic scales. Satisfying this phenomenology is a requirement if dark matter,
perhaps as invisible classical fields, could be correct here too. "Dark energy"
{\it might} be explained by a graviton-mass-like effect, with associated
Compton wavelength comparable to the radius of the visible universe. We
summarize significant mass limits in a table.
