  The basic conceptual picture and theoretical basis for development of
transport equations in porous media are examined. The general form of the
governing equations is derived for conservative chemical transport in
heterogeneous geological formations, for single realizations and for ensemble
averages of the domain. The application of these transport equations is focused
on accounting for the appearance of non-Fickian (anomalous) transport behavior.
The general ensemble-averaged transport equation is shown to be equivalent to a
continuous time random walk (CTRW) and reduces to the conventional forms of the
advection-dispersion equation (ADE) under highly restrictive conditions.
Fractional derivative formulations of the transport equations, both temporal
and spatial, emerge as special cases of the CTRW. In particular, the use in
this context of L{\'e}vy flights is critically examined. In order to determine
chemical transport in field-scale situations, the CTRW approach is generalized
to non-stationary systems. We outline a practical numerical scheme, similar to
those used with extended geological models, to account for the often important
effects of unresolved heterogeneities.
