The most widely used classifications of limestones are now thirty years old and our appreciation of the diagenetic effects on limestone textures is now much greater. A revision of the classifications of Dunham (1962) and Embry and Klovan (1971) is offered and new "diagenetic" categories are proposed. The confusing term lime mudstone is replaced by calcimudstone. Two categories of diagenetic textures are recognized: non-obliterative and obliterative. The former contains limestones which are almost wholly composed of diagenetic cement (cementstones) and those whose fabric is the result of intergranular pressure solution (condensed and fitted grainstones). Obliterative categories include limestones and dolomites whose original fabric has been destroyed; sub-categories include sparstones (or dolosparstones) (crystals > 10 μm in size) and microsparstones (dolomicrosparstones) (crystals 4-10 μm in size) and dolomicrostones crystals (< 4 μm in size). Many diagenetic processes can produce fabrics which mimic depositional ones and these are reviewed.