Indexable cutting unit heads for external turning are used as part of modular tool system in turning operations that size, shape, and add features to workpieces. They perform like solid turning tools, but mount to a compatible quick-change toolholder. The toolholder attaches to a lathe or CNC turning machine that rotates workpieces against the cutting head. These cutting heads can be replaced without removing the toolholder from the machine. The heads hold multi-edged inserts that can be rotated (indexed) to expose a fresh cutting edge when the old one dulls. The inserts can be exchanged for new ones of the same style or a different style that's compatible with the cutting head. Indexable turning tools require fewer tool changes than solid tools in high-volume metalworking and fabrication applications with high speeds, high feeds, and difficult-to-machine materials.