Method and apparatus for utilizing the vascular system as a conduit to reach other vascular and extravascular locations within the body. Included are methods for revascularization wherein the extravascular passageways are formed to permit blood flow between vascular locations. Also included are methods for performing transvascular interstitial surgery (TVIS) wherein extravascular passageways are formed from a blood vessel to another vascular or non-vascular intracorporeal location. Also disclosed are devices usable for forming extravascular passageways in accordance with the invention, or for modifying, valving, maintaining or closing such passageways.