Much progress has been made toward understanding the fundamental dynamics of turbulent transport in the presence of sheared flows. The insights have, among other methods, come from following Lagrangian trajectories using both gyrokinetic simulations of ITG turbulence and fluid models of drift-wave turbulence. Using these tools as well as the more standard measures, the impact of both sheared flows and simple diamagnetic drifts on the dynamics of the transport is investigated using numerical simulations of 2D-turbulence in slab geometry with the BETA code and in 3-D turbulence with the UCAN gyrokinetic code. The changes in the dynamics with these flows is found to be very significant with the transport in some cases becoming rather non-diffusive. The various impacts of flows on turbulent transport will be reviewed and the new transport dynamics and their possible uses will be discussed.