Abstract: Methods and devices using magnetic force to form an anastomosis between hollow bodies. End-to-side, side-to-side and end-to-end anastomoses can be created without using suture or any other type of mechanical fasteners, although such attachment means may be used in practicing some aspects of the invention. Magnetic anastomotic components may be attached to the exterior of a vessel, e.g., by adhesive, without extending into the vessel lumen. Various magnetic component configurations are provided and may have different characteristics, for example, the ability to match the vessel curvature or to frictionally engage the vessel.