We are developing infinite and finite packings of colloidal spheres to serve as the basis for making new optical and porous materials. Infinite packings are created by exploiting the equilibrium phase behavior or hard-sphere colloids. Finite packings are created by encapsulating colloidal spheres in small liquid emulsion droplets. Removing liquid from the droplets leads to packings of spheres that minimize the second moment of the mass distribution. The structures of the packings range from sphere doublets, triangles, and tetrahedra to exotic polyhedra not found in infinite lattice packings, molecules, or minimum-potential energy clusters. The emulsion system presents a route to produce new colloidal structures and a means to study how different physical constraints affect symmetry in small parcels of matter.