  Fast reconnection of magnetic field in turbulent fluids allows magnetic field
to change its topology and connections. As a result, the traditional concept of
magnetic fields being frozen into the plasma is no longer applicable. The
diffusion of plasmas and magnetic field is enabled by reconnection and
therefore is termed "reconnection diffusion". We explore the consequences of
reconnection diffusion for star formation. In the paper we explain the physics
of reconnection diffusion both from macroscopic and microscopic points of view.
We quantify the reconnection diffusion rate both for weak and strong MHD
turbulence and address the problem of reconnection diffusion acting together
with ambipolar diffusion. In addition, we provide a criterion for correctly
representing the magnetic diffusivity in simulations of star formation. We show
that the role of the plasma effects is limited to "breaking up lines" on small
scales and does not affect the rate of reconnection diffusion. We address the
existing observational results and demonstrate how reconnection diffusion can
explain the puzzles presented by observations, in particular, the observed
higher magnetization of cloud cores in comparison with the magnetization of
envelopes. We also outline a possible set of observational tests of the
reconnection diffusion concept and discuss how the application of the new
concept changes our understanding of star formation and its numerical modeling.
Finally, we outline the differences of the process of reconnection diffusion
and the process of accumulation of matter along magnetic field lines that is
frequently invoked to explain the results of numerical simulations
