A medical device is described comprising a biodegradable terephthalate copolymer comprising the recurring monomeric units shown in formula I: wherein R is a divalent organic moiety; R′ is an aliphatic, aromatic or heterocyclic residue; x is ≧1; and n is 3-7, 500, where the biodegradable polymer is sufficiently pure to be biocompatible and is capable of forming biocompatible residues upon biodegradation. Compositions containing the copolymers and biologically active substances, articles useful for implantation or injection into the body fabricated from the compositions, and methods for controllably releasing biologically active substances using the copolymers, are also described.