Non-equilibrium ionization is an important phenomenon 
related
to many astrophysical processes, such as rapid
heating or cooling,  in which gas may be under-ionized 
or over-ionized.
It is seen in a variety of astrophysical scenarios,
from the small scale such as massive star winds, 
accretion flows in
X-ray binaries, stellar cluster winds,  shocks in SNR,
to the large scale such as galactic superwinds, AGN 
outflows, and the
shock flows in the intergalactic medium. However, 
current modeling is
limited by the equilibrium ionization assumption.

I will emphasize the important role of the non-
equilibrium ionization
in the theoretical modelings for various plasmas. The 
generalized
NEI code will be introduced both for the collisional 
ionization and
photoionization. In addition, I will review the updated 
atomic database 
and atomic processes which are important for the non-
equilibrium plasma.
The applications of our NEI code in accretion disk corona 
of HerX-1,
line diagnostics in SNR N132D, warm-hot intergalactic 
medium
will be presented.