Six different theories of particle transport and flow-driven currents are discussed. These include the classical, neoclassical and four phenomenological models based on turbulence. The theoretical results are compared and contrasted. In particular, two different, turbulence-based, equivalent versions of the toroidal Ohm's law are obtained. The possibility of experimentally distinguishing between the phenomenological models is discussed. In two of the phenomenological models the anomalous particle transport is necessarily related to anomalous flow-driven currents (i.e. enhanced above the neoclassical bootstrap current), and to anomalous inward pinches.