In this paper we examine two problems numerically. The first problem concerns the structure and evolution of MHD turbulence. Simulations are presented which show evidence of forming a turbulent cascade leading to a self-similar phase and eventually a decay phase. Several dynamical diagnostics of interest are tracked. Spectra for the kinetic and magnetic energies are presented. The second problem consists of the formation of pre-protostellar cores in a turbulent, magnetized molecular clouds. It is shown that the magnetic field strength correlates positively with the density in keeping with observations. It is also shown that the density and magnetic fields organize themselves into filamentary structures. Through the construction of simulated channel maps it is shown that accretion onto the cores takes place along the filaments. Thus a new dynamical process is reported for accretion onto cores. We have used the first author's RIEMANN code for astrophysical fluid dynamics for all these calculations.