Indexable thread-cutting unit heads are used with lathes or CNC turning machines as part of a modular thread-turning tool system to cut threads on a workpiece. These threading heads mount to a compatible quick-change toolholder, which allows the head to be swapped out for a boring or turning head while the toolholder remains in the machine. The heads hold replaceable thread-turning inserts, which typically have multiple cutting edges so they can be rotated (indexed) to expose a fresh cutting edge when the old one dulls. The inserts can be replaced with new ones of the same type or different types without removing the toolholder or tool body from the machine. Indexable threading 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.