Spherical packing is an interesting problem in mathematics and physics. In particular, spherical packing is intimately related to the structure of ordered phases. The observation of ordered phases in hard-condensed matter systems such as metallic alloys has a long history in materials physics. In recent years, intricate periodic and aperiodic order has emerged in a host of soft matter systems including supramolecular assemblies, surfactants and block copolymers. The occurrence of complex ordered phases in these diverse systems underscores the universality of emergent order in condensed matter. The richness of the phase behavior is exemplified by block copolymers. Recent experimental and theoretical studies have revealed that non-classical ordered phases, such as quasicrystals and the Frank-Kasper phases, could emerge from block copolymers as equilibrium or metastable morphologies. As such, block copolymers provide an ideal system to study the origins and stability of periodic and aperiodic order in condensed matter physics. We have examined the occurrence of complex spherical packing phases in block copolymer systems using the self-consistent field theory. Our study reveals that one key mechanism of forming complex spherical phases is the conformational asymmetry of the blocks. Furthermore, we have predicted that the segregation of different polymeric species in block copolymer blends provides another mechanism to stabilize spherical packing phases with very different sized-spherical domains. In my presentation, I will summarize recent theoretical and experimental progresses on this fascinating topic and discuss possible future research directions.