Methods, devices, and systems for a) revascularization and/or b) performing other medical procedures at vascular or non-vascular intracorporeal locations within a mammalian body. The methods generally comprise the formation of at least one extravascular passageway from a blood vessel to a vascular or non-vascular target location. In the revascularization methods the extravascular passageway is utilized for blood flow. In the medical procedure methods the extravascular passageway is utilized as a conduit for accessing or performing procedures at the vascular or non-vascular target location. Also disclosed are catheter devices and systems which are useable to form the extravascular passageways of the invention, as well as apparatus for modifying, maintaining and/or closing such extravascular passageways.