A polyaxial screwdriver for inserting a bone screw in a vertebra. A polyaxial bone screw assembly includes a coupling element. When a screw engaging end of the polyaxial screwdriver is lowered on the head of the bone screw, the complimentary surfaces of the screw engaging end of the screwdriver and the head of the screw self-align. A ratchet mechanism formed in the screwdriver provides progressive and automatic locking of the polyaxial screwdriver to the coupling element and prevents the accidental unthreading from the coupling element. In another embodiment of the polyaxial screwdriver, a collet slides over the outside surface of the upper end of the coupling element and locks on to the coupling element. In yet another embodiment of a polyaxial screwdriver, the outer sleeve of the polyaxial screwdriver has a split end that securely engages the coupling element.