The present invention provides, in certain aspects, medical devices deliverable into passageways and other open spaces in the body. In one embodiment, the invention provides a fistula plug for delivery into a fistula tract. This fistula plug includes an elongate plug body, and a removable core material that is received in the plug body and effective to increase the column strength of the plug body. The plug body may be formed with one or more of a variety of biocompatible materials including some that are naturally derived and some that are non-naturally derived. The present invention also provides apparatuses and methods for delivering these and other medical devices into the body. One such apparatus includes a fistula plug having a plug body, and a removable delivery device received in the plug body, wherein the delivery device is effective to deliver the plug body into a fistula tract when advanced therethrough.