Materials comprised of "designer" nanoscale building blocks organized into structures with novel functionality represent the next frontier for materials research and development. Breakthroughs in synthesis and fabrication techniques over the past few years have produced an exquisite library of building blocks of nearly arbitrary shape and composition. Still, control of the assembly of these building blocks into target structures is required for these new "atoms" and "molecules" to form the foundation for next-generation materials in applications ranging from energy to medicine. Theory, modeling and simulation are critical tools in this quest. Needed for progress are useful schemes for classifying anisotropy and its impact on assembly; insight into synthesis and fabrication methods for producing designed particles; efficient computational methods for predicting assemblies of building blocks with arbitrary anisotropy; and new methods for characterizing the degree and type of order in assembled phases of anisometric shapes. In this talk* **, we present examples of computer simulation studies of self-assembly of a rich array of structures from "patchy" and "tetnered" nanoparticles and colloids that demonstrate how various anisotropy attributes may be exploited and combined for self-assembly. We describe a new computational algorithm that rapidly approximates ground state structures of strongly-interacting particles with arbitrary anisotropy, and which shows how small changes in particle patchiness and shape can produce large changes in macrostructure. Finally, we introduce new order parameters schemes for characterizing the local translational and orientational order of assembled phases formed from complex shapes.

* In collaboration with A.H.Akbari, E.R. Chan, T. Chen, P. Ghorai, M.A. Horsch, C.R. Iacovella, E. Jankowski, A.S. Keys, T.D. Nguyen, C. Phillips, A. Santos, T. Sheh, C. Singh, S. Teich-McGoldrick, X. Zhang, Z.L. Zhang, and N.A. Kotov, M.J. Solomon, and F. Stellacci.

**Funded by DoE, NSF, DoEd, AFOSR, NASA, and the McDonnell Foundation