Several statistical theories of the transport of a passive scalar quantity make use of a Green's function and statistical properties of the fluid velocity field. The theories are applied to the problems of mean gradient transport in a turbulent fluid and of turbulent transport to a wall or a fluid interface. For the case of mass transfer by a uniform mean concentration gradient in homogeneous turbulence, a weak mixing hypothesis leads to results similar to those of Kraichnan's direct interaction approximation (D1A). Further use of a smoothing hypothesis leads to an algebraic expression for the eddy diffusivity which compares well with the DIA and with laboratory experiments.