  We consider in this work the asymptotics of a Maxwell field in Schwarzschild
and Kerr spacetimes. In any subextremal Kerr spacetime, we show energy and
pointwise decay estimates for all components under an assumption of a basic
energy and Morawetz estimate for spin $\pm 1$ components. If restricted to
slowly rotating Kerr, we utilize the basic energy and Morawetz estimates proven
in an earlier work to further improve these decay estimates such that the total
power of decay for all components of Maxwell field is $-7/2$. In the end,
depending on if the Newman--Penrose constant vanishes or not, we prove almost
sharp Price's law decay $\tau^{-5+}$ (or $\tau^{-4+}$) for Maxwell field and
$\tau^{-\ell -4+}$ (or $\tau^{-\ell -3+}$) for any $\ell$ mode of the field
towards a static solution on a Schwarzschild background. All estimates are
uniform in the exterior of the black hole.
