Nanotechnology is touted as the next logical sequence in technological evolution. This has led to a substantial surge in research activities pertaining to the development and fundamental understanding of processes and assembly at the nanoscale. Both top-down and bottom-up fabrication approaches may be used to realize a range of well-defined nanostructured materials with desirable physical and chemical attributes. Among these, the bottom-up self-assembly process offers the most realistic solution toward the fabrication of next-generation functional materials and devices. Here, we present a comprehensive review on the physical basis behind self-assembly and the processes reported in recent years to direct the assembly of nanoscale functional blocks into hierarchically ordered structures. This paper emphasizes assembly in the synthetic domain as well in the biological domain, underscoring the importance of biomimetic approaches toward novel materials. In particular, two important classes of directed self-assembly, namely, (i) self-assembly among nanoparticle-polymer systems and (ii) external field-guided assembly are highlighted. The spontaneous self-assembling behavior observed in nature that leads to complex, multifunctional, hierarchical structures within biological systems is also discussed in this review. Recent research undertaken to synthesize hierarchically assembled functional materials have underscored the need as well as the benefits harvested in synergistically combining top-down fabrication methods with bottom-up self-assembly.