This session is intended to bring together new ideas and theories for the transport of water, sediment, pollutants, and biota on the Earth's surface acknowledging the presence of heterogeneities over a broad range of scales. Of special interest is transport on hillslopes, rivers, and channel networks and topics include: methods by which the spatial organization of channel networks can be exploited to improve environmental prediction, the effect of connectivity on transport processes, non-local transport theories to accommodate heavy-tailed distributions of velocities and/or residence times, generalized random walk constructs for sediment transport in channels and channel networks, new theories for transport on fractal trees, scale-dependence and scale-invariance in parameterization of transport laws, emergent scaling in landscape evolution models, and other theories for treating nonlinear transport and complexity in landscape evolution.