A graphics virtual texturing system in which textures stored in a storage medium of a host system are divided into respective pages that are then loaded into a local memory of a graphics processing system for use. If the texture page that is required for performing a texturing operation at an originally desired level of detail (52) is not present in the local memory of the graphics processing system (53), the virtual texture lookup process loops back to try to sample the texture at an increased level of detail (55), and so on, until texture data that can be used is found in the local memory of the graphics processing system (53). This allows the texturing operation to proceed using texture data for the texel positions in question from a higher level (less detailed) mipmap in place of the originally desired texture data.