A texture cache comprises at least two banks of cache storage to cache texels for processing in texture mapping operations. Access to the cached texels corresponding to a given chunk of texels of a given texture image is controlled according to a selected bank mapping selected from two or more bank mappings supported by the texture cache access control circuitry. Each bank mapping corresponds to a different mapping of the respective texels within the given chunk to the banks of cache storage. In at least one operating mode, the selected bank mapping is selected for the given chunk of texels of the given texture image depending on: at least one of first/second chunk position coordinates associated with the given chunk of texels; and at least one further texture attribute associated with the given texture image.