  We describe how power operations descend through homotopy limit spectral
sequences. We apply this to describe how norms appear in the $C_2$-equivariant
Adams spectral sequence, to compute norms on $\pi_0$ of the equivariant
$KU$-local sphere, and to compute power operations for the $K(1)$-local sphere.
An appendix contains material on equivariant Bousfield localizations which may
be of independent interest.
