The present invention provides implantable devices and associated methods forinterconnecting human vessels in a side-to-side or an end-to-side arrangement rapidly, safely and in a minimally invasive manner. The devices comprises at least a first segment, a second component, and a flow opening between the at least one segment and the second component when operatively used. The first segment is flexible and has physical and mechanical properties which allow it to be easily inserted into a vessel, to conformably seal with the inside wall of the vessel and to be resistant to dislodging from the vessel. The second component may comprise a second segment having the same or a similar configuration as the first segment or may be a tubular member which extends from the first segment. The first and second segments are flexible for easy insertion into an incision made within the side of each vessel. Upon release from a constricted state, each flexible segment subsequently conforms to the interior walls of a vessel to provide a sealing contact along the contact surface of the segment inserted within. The tubular member is configured to be inserted into a transected end of a vessel. The flow opening provides fluid interconnectivity between the vessels connected by the implanted devices. The devices are configured so as to: (1) not impede flow inside a vessel; (2) prevent leakage from the incisions within the vessels; and (3) apposition the vessels toward each other allowing the vessels to heal together so that flow in one vessel may flow to the other.