The present invention pertains to an apertured polymeric film web material provided with a multiplicity of substantially three dimensional surface structures and provided with a multiplicity of fluid transport apertures. In one embodiment, the fluid transport apertures are formed using a process that substantially preserves the integrity of the surface structures. Methods of producing webs are also disclosed. The present invention also includes multi-ply composite structures formed using apertured polymeric film web materials and a sub-ply. The present invention also pertains to absorbent articles which preferably include a topsheet in accordance with the present invention, a backsheet secured to the topsheet, and an absorbent core positioned between the topsheet and the backsheet.