Fluid flow and transport through porous materials are complex phenomena. X-ray tomography provides a nonintrusive way of imaging the three dimensional structure of porous materials. Studying porous media at the pore scale enables investigation of the porous space at micro and nanometer scale. I have developed an algorithm that robustly partitions the void volume into a set of discrete pores. The ambiguity in deciding where to draw the partitioning boundaries in space can be handled by a form of logic called fuzzy logic. The result is a simplified network of pores, which can be used to estimate the flow properties of the sample. The statistical properties of such networks can also be used to cluster rocks of different types. The most important hydrocarbon reservoir rocks and aquifer rocks in the world are often fractured. Successful reservoir or aquifer characterization requires a detailed picture of the fracture network. I developed a fast algorithm to automatically detect and extract fracture networks in the three dimensional tomography images of rocks. Using context aware image processing operations, I separated the 3D structure of the fracture network from the rest of pores in the rock. The proposed algorithm is capable of consistently estimating the fractal dimension and fracture aperture distribution of the fracture network even for noisy or low resolution images. To study the properties of the internal structure of the rocks imaged by X-ray tomography, I simulated the particle diffusion within the pores. Millions of digital particles were suspended in a digital model of the rock and the diffusion process was simulated by random walk of the particles. Analysing the behaviour of mean squared displacement of the particles at the early time and late time, it is possible to estimate the surface to volume ratio, tortuosity and permeability of the sample