In one aspect the present invention provides biodegradable, porous structures that each include a structural framework, wherein the structural framework includes: (a) a solidified mixture of polymer molecules and amino acid molecules, wherein at least some of the amino acid molecules are linked to other amino acid molecules within the framework; and (b) a multiplicity of interconnected spaces defined by the structural framework. In some embodiments, the porous structures of the invention are adapted to physically support the growth of living cells in vitro or in vivo, and can be used to grow living tissue and/or living organs. The present invention also provide methods for making the biodegradable, porous structures of the invention.