Embolectomy catheters, rapid exchange microcatheters, systems and methods for removing obstructive matter (e.g., thrombus, thromboemboli, embolic fragments of atherschlerotic plaque, foreign objects, etc.) from blood vessels. This invention is particularly useable for percutaneous removal of thromboemboli or other obstructive matter from small blood vessels of the brain, during an evolving stroke or period of cerebral ischemia. In some embodiments, the embolectomy catheters of this invention are advanceable over a guidewire which has been pre-inserted through or around the obstructive matter. Also, in some embodiments, the embolectomy catheters include obstructive matter capturing receptacles which are deployable from the catheter after the catheter has been advanced at least partially through the obstructive matter. Such obstructive matter capturing receptacles may include i) at least one proximal strut which are designed to be retractable through a blood clot and ii) a distal matter-receiving portion which is designed to prevent a blood clot from passing therethrough.In particular, the embolectomy catheter may be a rapid exchange embodiment.