  Astrophysical fluids are turbulent, magnetized and frequently partially
ionized. As an example of astrophysical turbulence, the interstellar turbulence
extends over a remarkably large range of spatial scales and participates in key
astrophysical processes happening in different ranges of scales. A significant
progress has been achieved in the understanding of the magnetohydrodynamic
(MHD) turbulence since the turn of the century, and this enables us to better
describe turbulence in magnetized and partially ionized plasmas. In fact, the
modern revolutionized picture of the MHD turbulence physics facilitates the
development of various theoretical domains, including the damping process for
dissipating MHD turbulence and the dynamo process for generating MHD turbulence
with many important astrophysical implications. In this paper, we review some
important findings from our recent theoretical works to demonstrate the
interconnection between the properties of MHD turbulence and those of turbulent
dynamo in a partially ionized gas. We also briefly exemplify some new tentative
studies on how the revised basic processes influence the associated outstanding
astrophysical problems in, such as, magnetic reconnection, cosmic ray
scattering, magnetic field amplification in both the early and the present-day
universe.
