Abstract: The hydraulic conductivity is one of the most important parameters for describing the physical characteristics of porous media.The spatial variability of hydraulic conductivity has an important effect on water movement and solute transport in porous media.The methods based on spatial random fields fail to describe the spatial variation of hydraulic conductivity with multi-scales.Therefore a new method is developed in recent years on the basis of fractal theory,with which fractional Brown motion(fLm)and fractal Levy motion(fLm)are applied to study the variability of hydraulic conductivity without permanent integral scale.The main objective of this paper is to review the methods based on the fractal theory,and to analyze the relationship between the spatial variability of hydraulic conductivity and scale-effect of solute dispersivity and its application to describe water movement and solute transport.