Methods and materials for making complex, living, vascularized tissues for organ and tissue replacement, especially complex and/or thick structures, such as liver tissue is provided. Tissue lamina is made in a system comprising an apparatus having (a) a first mold or polymer scaffold, a semi-permeable membrane, and a second mold or polymer scaffold, wherein the semi-permeable membrane is disposed between the first and second molds or polymer scaffolds, wherein the first and second molds or polymer scaffolds have means defining microchannels positioned toward the semi-permeable membrane, wherein the first and second molds or polymer scaffolds are fastened together; and (b) animal cells. Methods for producing complex, three-dimensional tissues or organs from tissue lamina are also provided.