This chapter discusses the potential for obtaining order-of-magnitude-type constraints on the permeability structure of unconsolidated alluvial aquifers through a variety of non-standard geophysical measurements. Knowledge of the permeability distribution within an aquifer is a key prerequisite for reliable predictions of fluid flow and contaminant transport. This information is in turn critical for the effective protection, remediation and sustainable management of the increasingly scarce and fragile surficial groundwater resources in densely populated and/or highly industrialized regions throughout the world. Geophysical constraints with regard to the permeability structure are considered to be particularly valuable because some of them have the potential to bridge the inherent gap in terms of resolution and coverage that exists among traditional hydrological methods, such as core analyses and tracer or pumping tests. Although standard geophysical exploration techniques cannot in general provide direct information on the permeability structure of the probed medium, there are less conventional approaches that are expected to exhibit some more or less direct sensitivity to the permeability structure. Probably the most promising techniques for this purpose are analyses of the attenuation of Stoneley waves and seismic body waves, nuclear magnetic resonance techniques, induced polarization measurements, and gamma logs. Whereas the attenuation of seismic waves in saturated porous media is known to be more or less directly related to the permeability structure of the probed medium, and nuclear magnetic resonance techniques are sensitive to the water content and the pore size, induced polarization measurements and gamma logs exhibit a less direct relation to the permeability structure of unconsolidated sediments via their sensitivity to the grain size and/or the specific surface of the pore spaces.