The turbulent diffusion coefficient is calculated using two different approaches, one involving test particles and the other involving the dynamically-passive convected field. The particle approach is Lagrangian in character. The version the author offers is a refinement of the classical version employing new types of independence hypothesis, Gaussianity-implying hypothesis and diffusion hypothesis. The field approach is Eulerian in character. The version offered is a slight modification of the classical version involving transient effects. When the transient effects are no longer important both approaches give the same results, and rely on the same set of restrictions. The fluctuation amplitudes and Lagrangian correlation times that are not necessarily very small are considered. The problems associated with the zero micro-diffusivity limit are addressed.