A method of making a composite living fiber is described that includes the steps of contacting a fiber strand with an aqueous solution comprising cells, alginate, and a non-alginate hydrogel precursor to coat the fiber; crosslinking the alginate of the coated fiber; and crosslinking the non-alginate hydrogel precursor to form a composite living fiber. Composite living fibers made by this method, and tissue scaffolds made of composite living fibers, are also described.