Texture filtering is applied to a texture represented with a mipmap comprising a plurality of levels, wherein each level of the mipmap comprises an image representing the texture at a respective level of detail. A texture filtering unit has minimum and maximum limits on an amount by which it can alter the level of detail when it filters texels from an image of a single level of the mipmap. The range of level of detail between the minimum and maximum limits defines an intrinsic region of the texture filtering unit. If it is determined that a received input level of detail is in an intrinsic region of the texture filtering unit, texels are read from a single mipmap level of the mipmap, and the read texels from the single mipmap level are filtered to determine a filtered texture value representing part of the texture at the input level of detail. If it is determined that the received input level of detail is in an extrinsic region of the texture filtering unit: texels are read from two mipmap levels of the mipmap, and the read texels from the two mipmap levels are processed to determine a filtered texture value representing part of the texture at the input level of detail.