The present invention is directed to novel implantable or insertable medical devices that provide controlled release of a therapeutic agent. According to an embodiment of the present invention, a therapeutic-agent-releasing medical device is provided, which comprises: (a) an implantable or insertable medical device; (b) a release layer disposed over at least a portion of the implantable or insertable medical device; and (c) a therapeutic agent. The release layer comprises a maleic anhydride polymer selected from (i) a maleic anhydride copolymer and (ii) a maleic anhydride graft polymer. The release layer regulates the rate of release of the therapeutic agent from the medical device upon implantation or insertion of the device into a patient. The present invention is also directed to methods of forming the above implantable or insertable medical devices, methods of administering a therapeutic agent to a patient using such devices, and methods of modulating the release of therapeutic agent from such devices.