Mechanical thrombectomy apparatuses (devices, systems, etc.) and methods for positioning them within a vessel and using them to remove a thrombus, e.g., clot, from within a vessel. In particular, described herein are methods of advancing an inverting tractor thrombectomy apparatus having a tractor comprising a flexible tube of material that inverts over itself as it rolls over a distal end opening of an elongate inversion support by extending the tractor region and/or a puller coupled to the tractor distally beyond the end of the catheter. Also described herein are power-driven mechanical thrombectomy apparatuses.