Catheter devices having low profile shafts and laterally deployable members (e.g., cannulas, needles, etc.) that may be extended or advanced laterally from the catheter shaft. Also disclosed are methods for bypassing a vascular obstruction (e.g., a chronic total occlusion or other full or partial obstruction) wherein a guidewire is entrapped in a subintimal space adjacent to the obstruction. A catheter of the foregoing character is advanced over the entrapped guidewire and into the subintimal space. The laterally deployable member is then advanced or extended from the subintimal space back into the true lumen of the blood vessel distal to the obstruction. A second guidewire is then advanced through or along the laterally deployable member. The catheter and first guidewire are then removed and one or more working device(s) (balloons, atherectomy devices, stents, etc.) is/are advanced over the second guidewire and used to establish a subintimal bypass channel through which blood may flow around the obstruction.
