An implantable or insertable medical device which comprises (a) a therapeutic agent and (b) a polymeric release region that controls the release of the therapeutic agent upon administration to a patient. The polymeric release region comprises a radiation-crosslinked polymer, and the polymeric release region is crosslinked with a radiation dose of at least 10,000 rads. The radiation-crosslinked polymer can be, for example, a radiation-crosslinked methylene-containing polymer. The polymeric release region can be, for example, (a) a carrier region that comprises the therapeutic agent or (b) a barrier region that is disposed over a therapeutic-agent-containing region that comprises the therapeutic agent. The present invention is further directed to methods of forming such medical devices, methods of releasing a therapeutic agent within a patient using such medical devices, and methods of modulating the release of a therapeutic agent from such medical devices.