We investigate the pore network geometry and permeability of six natural sandstones and carbonate rocks. Using 3D microtomographic images, we segment each rock sample into three phases: Solid matrix of grains, macropores containing void spaces, and a third microporous phase containing nanometer-sized pores beyond the resolution of the image. In the majority of our samples, the microporosity exists inside cements deposited as a secondary phase along the surface of grains. Within the macropores, the pore radius, coordination number, throat radius, and throat length display a power law relation with porosity. We also find that the permeability of the aggregate depends on the porosity following the relation k = k 0 φ 3.32 , where log k 0 = 5.52 (mD). The fraction of connected porosity shows a strongly non-linear reduction with an increase in the volume fraction of microporous cement.