In one embodiment, a device for closing or occluding ASDs and PFOs, or other bodily passageways, includes a circumferential frame, a sheet of biocompatible material attached to the frame, and at least one anchor attached to the sheet of biocompatible material. In another embodiment, the closure device includes a circumferential frame, at least one crossbar extending across and attached to the frame, at least one anchor connected to at least one crossbar and at least one sheet of biocompatible material (such as ECM material) attached to the frame. The anchor includes at least one grasping member having a structure, such as a wired loop, which is configured for releasable attachment to a delivery release member, which facilitates delivery of a closure device collapsibly disposed in a delivery catheter. Alternatively, one or more anchor end pairs may be connected to a delivery bar enhancing delivery and retrieval of the device.