Finite materials systems of reduced sizes exhibit specific forms of aggregation, phases, structures and morphologies, quantized electronic shell structures, dimensionality cross-over, and size-dependent evolutionary patterns, which are manifested in unique, nonscalable, size-dependent physical and chemical properties. Indeed, when the dimensions of materials structures are reduced to the nanoscale, emergent phenomena often occurs, that are not commonly expected, or deduced, from knowledge gained at larger sizes. Discovery, characterization, understanding and possible utilization of such emergent behavior of materials in the nanoscale are among the major challenges of modern materials science. Progress in theses directions is greatly facilitated, or even predicated, by synthesis, fabrication, separation and measurements of atomically precise nanostructures, and by theoretical investigations of their unique structural, chemical and physical properties. Computer-based quantum computations, simulations and emulations, are tools of discovery which enable uncovering emergent behavior in the nanoscale. In this talk we employ such simulations, often in conjunction with laboratory experiments, to explore some of the origins that underlie the unique behavior of size-selected materials in the nanoscale, and highlight computational microscopy investigations of nanoscale phenomena in diverse systems, ranging from: nanoscale liquid jets and bridges, droplet electro-crystallization, nanoclusters and machine-like response of their self-assembled superlattices, to symmetry-breaking manifested in formation of highly-correlated Wigner molecules in electron quantum dots, and exact numerical emulations of many-body microscopic hamiltonians, suggesting the employment of finite ultracold fermionic atom systems in fundamental studies of quantum magnetism, entanglement, and high-T_c superconductivity.