Methods and apparatuses involving biocompatible structures for tissue engineering and organ replacement and, more specifically, biocompatible structures formed by three-dimensional fabrication, are described. In some embodiments, the biocompatible structures are scaffolds for cells that can be used as tissue engineering templates and/or as artificial organs. The structures may be three-dimensional and can mimic the shapes and dimensions of tissues and/or organs, including the microarchitecture and porosities of the tissues and organs. Pores in the structure may allow delivery of molecules across the structure, and may facilitate cell migration and/or generation of connective tissue between the structure and its host environment. Structures of the invention can be implanted into a mammal and/or may be used ex vivo as bioartificial assist devices.