An arteriovenous shunt assembly including a shunt having a hollow bore between open first and second ends thereof and a valve slidably disposed through the hollow bore. The valve includes means for retaining the valve in a closed position or in any of various selected open positions that provide corresponding different rates of blood flow through the shunt assembly. In some embodiments, the AV shunt assembly is self-expandable from a collapsed tow-profile configuration employed during transluminal delivery. The valve position in the hollow bore may be adjusted in vivo by inflating a catheter balloon in a blood vessel to bear against an end of the valve. Methods for using the shunt assembly are also disclosed.