Methods and apparatus for delivery of substances or apparatus to target sites located outside blood vessels within the body of a human or animal patient. A vessel wall penetrating catheter is inserted into the vasculature, positioned and oriented within a blood vessel near the target extravascular site and a penetrator is advanced from the catheter so as to penetrate outwardly through the wall of the blood vessel in the direction of the target site. Thereafter, a delivery catheter is passed through a lumen of the penetrator to the target site. A desired substance or apparatus is then delivered to or obtained from the target site. In some applications, the penetrator may be retracted into the vessel wall penetrating catheter and the vessel wall penetrating catheter may be removed, leaving the delivery catheter in place for chronic or continuous delivery of substance(s) to and/or obtaining of information or samples from the target site. Alternatively, a delivery catheter having an occlusion member or balloon may be advanced into a vein or venule and the occlusion member or balloon may be used to occlude the lumen of the vein or venule during and after injection of a substance through the catheter, such that the substance will not be carried away by normal venous blood flow and will remain in the vein or venule for a sufficient period of time to have its intended effect (e.g. to enter adjacent tissues through capillary beds drained by that vein or venule).