The invention provides high molecular weight, crystalline or semi crystalline biodegradable and biocompatible poly(ester urea) (PEU) polymers useful for making vascular stents and hard tissue replacement implants, such as bone substitutes. The PEU polymers are based on α amino acids and are made by a polycondensation reaction. PEU polymer compositions can contain a therapeutic diol incorporated into the polymer backbone that is released from such an implant in situ. Bioactive agents, such as analgesics, antibiotics, and the like, can also be covalently attached to certain PEU polymers for release into tissue surrounding an implant during biodegradation of the polymer.