The fabrication of cell-laden structures with anisotropic mechanical properties while having a precise control over the distribution of different cell types within the constructs is important for many tissue engineering applications. Automated textile technologies for making fabrics allow simultaneous control over the color pattern and directional mechanical properties. The use of textile techniques in tissue engineering, however, demands the presence of cell-laden fibers that can withstand the mechanical stresses during the assembly process. Here, the concept of composite living fibers (CLFs) in which a core of load bearing synthetic polymer is coated by a hydrogel layer containing cells or microparticles is introduced. The core thread is drawn sequentially through reservoirs containing a cell-laden prepolymer and a crosslinking reagent. The thickness of the hydrogel layer increases linearly with to the drawing speed and the prepolymer viscosity. CLFs are fabricated and assembled using regular textile processes including weaving, knitting, braiding, winding, and embroidering, to form cell-laden structures. Cellular viability and metabolic activity are preserved during CLF fabrication and assembly, demonstrating the feasibility of using these processes for engineering functional 3D tissue constructs.