Abstract： inite 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, non-scalable, 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 deducible, from knowledge gained at larger sizes. Computer-based quantum computations, simulations and emulations, are tools of discovery which enable uncovering emergent behavior in the nanoscale. In this talk we employ simulations, often in conjunction with laboratory experiments, to explore the origins of the unique behavior of size-selected materials systems in the nanoscale. We illustrate such computational microscopy investigations in diverse areas, ranging from formation and quantized transport in nanowires, stability and stochastic hydrodynamics of nanoscale jets and liquid junctions, and machine-like response emerging in self-assembled superlattices comprised of atomically-precise nanoclusters, to spontaneous symmetry breaking manifested in formation of highly-correlated Wigner molecules in electron quantum dots, quantum space-time crystals, and exact numerical simulations of many-body microscopic Hamiltonians, leading to the employment of finite ultracold atom systems in fundamental explorations of quantum magnetism, entanglement, matter-wave interferometry, and quantum-optics phenomena emulated with interacting ultracold atoms.