  Contributions of a spin 0 axion-like particle (ALP) to lepton dipole moments,
g-2 and EDMs, are examined. Barr-Zee and light-by-light loop effects from a
light pseudoscalar ALP are found to be capable of resolving the long-standing
muon g-2 discrepancy at the expense of relatively large ALP-gammagamma
couplings. The compatibility of such large couplings with direct experimental
constraints and perturbative unitarity bounds is discussed. Future tests of
such a scenario are described. For CP violating ALP couplings, the electron EDM
is found to probe much smaller, theoretically more easily accommodated ALP
interactions. Future planned improvement in electron EDM searches is advocated
as a way to not only significantly constrain ALP parameters but also, to
potentially unveil a new source of CP violation which could have far reaching
ramifications.
