  Building off of many recent advances in the subject by many different
researchers, we describe a picture of A-equivariant chromatic homotopy theory
which mirrors the now classical non-equivariant picture of Morava,
Miller-Ravenel-Wilson, and Devinatz-Hopkins-Smith, where A is a finite abelian
p-group. Specifically, we review the structure of the Balmer spectrum of the
category of A-spectra, and the work of Hausmann-Meier connecting this to MU_A
and equivariant formal group laws. Generalizing work of
Bhattacharya-Guillou-Li, we introduce equivariant analogs of v_n-self maps, and
generalizing work of Carrick and Balderrama, we introduce equivariant analogs
of the chromatic tower, and give equivariant analogs of the smash product and
chromatic convergence theorems. The equivariant monochromatic theory is also
discussed. We explore computational examples of this theory in the case of A =
C_2, where we connect equivariant chromatic theory with redshift phenomena in
Mahowald invariants.
