A classical ground-state configuration of a system of interacting particles is one that minimizes the system potential energy. In the laboratory, such states are produced by slowly cooling a liquid to a temperature of absolute zero, and usually the ground states are crystal structures. However, our theoretical understanding of ground states is far from complete. For example, it is difficult to prove what are the ground states for realistic interactions. I discuss recent theoretical/computational methods that we have formulated to identify unusual crystal ground states as well as disordered ground state [1,2,3,4]. Although the latter possibility is counterintuitive, there is no fundamental reason why classical ground states cannot be aperiodic or disordered.1) M. Rechtsman, F. H. Stillinger and S. Torquato, Synthetic Diamond and Wurtzite Structures Self-Assemble with Isotropic Pair Interactions , Physical Review E, vol. 75, 031403 (2007). 2) S. Torquato and F. H. Stillinger, "New Duality Relations for Classical Ground States," Physical Review Letters, vol. 100, 020602 (2008). 3) R. D. Batten, F. H. Stillinger and S. Torquato, "Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials," Journal of Applied Physics, vol. 104, 033504, (2008). 4) A. Scardicchio, F. H. Stillinger and S. Torquato, "Estimates of the Optimal Density of Sphere Packings in High Dimensions, Journal of Mathematical Physics, vol. 49, 043301 (2008).