This document summarizes research done at Lawrence Livermore National Laboratory on using 3D printing to create cellular materials with controlled architectures. It shows how printing ordered porous structures enables better control over the materials' mechanical properties compared to traditional random porous materials. In particular, it demonstrates that a "face centered tetragonal" structure exhibits different stress-strain behavior under compression and shear than a "simple cubic" structure, despite both having the same material composition and 50% porosity. This controlled architecture printing process could enable new material designs with targeted performance properties.