Devices and methods for delivering drugs and other therapeutic or diagnostic substances to desired locations within the bodies of human or non-human animal subjects. An implantable delivery device comprising a reservoir is initianlly attached to a deliver catheter or delivery tool and is introduced into the body and positioned at a desired site. A therapeutic or diagnostic substance is then introduced into the reservoir and the delivery catheter or deliver tool is then removed, leaving the implantable delivery device implanted within the body. The substance is then delivered from the reservoir at a rate that causes the desire diagnostic or therapeutic effect. Also provided are substance eluting stents that elute substance from a selected surface of the stent (e.g., the outer surface) but not from another surface of the stent (e.g., the inner surface).