Embolectomy catheters, rapid exchange microcatheters, systems and methods for removing clots or other obstructive matter (e.g., thrombus, thromboemboli, embolic fragments of atherosclerotic 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 with or over a guidewire which has been pre-inserted through or around the clot. Also, in some embodiments, the embolectomy catheters include clot removal devices which are deployable from the catheter after the catheter has been advanced at least partially through the clot. The clot removal device may include a deployable wire nest that is designed to prevent a blood clot from passing therethrough. The delivery catheter may include telescoping inner and outer tubes, with the clot removal device being radially constrained by the outer tube. Retraction of the outer tube removes the constraint on the clot removal device and permits it to expand to its deployed configuration. An infusion guidewire is particularly useful in conjunction with the embolectomy catheter, and permits infusion of medicaments or visualization fluids distal to the clot.