The flow in porous media has received a great deal of attention due to its importance and many unresolved problems in science and engineering such as geophysics, soil science, underground water resources, petroleum engineering, fibrous composite manufacturing, biophysics (tissues and organs), etc. It has been shown that natural and some synthetic porous media are fractals, and these media may be called fractal porous media. The flow and transport properties such as flow resistance and permeability for fractal porous media have steadily attracted much attention in the past decades. This review article intends to summarize the theories, methods, mathematical models, achievements, and open questions in the area of flow in fractal porous media by applying the fractal geometry theory and technique. The emphases are placed on the theoretical analysis based on the fractal geometry applied to fractal porous media. This review article shows that fractal geometry and technique have the potentials in analysis of flow and transport properties in fractal porous media. A few remarks are made with respect to the theoretical studies that should further be made in this area in the future. This article contains 220 references.