Cerium oxide (ceria)-based materials in the nanoscale regime are of significant fundamental and technological interest. Nanoceria in pure and doped forms has current and potential use in solid oxide fuel cells, catalysis, UV- screening, chemical mechanical planarization, oxygen sensors, and bio-medical applications. The characteristic feature of Ce to switch between the +3 and +4 oxidation states renders oxygen buffering capability to ceria. The ease of this transformation was expected to be enhanced in the nanoceria. In most the practical scenarios, it is necessary to have a stable suspension of ceria nanoparticles (CNPs) over longer periods of time. However, the existing literature is confined to short term studies pertaining to synthesis and property evaluation. Having understood the need for a comprehensive understanding of the CNP suspensions, this dissertation is primarily aimed at understanding the behavior of CNPs in various chemical and physical environments. We have synthesized CNPs in the absence of any surfactants at room temperature and studied the aging characteristics. After gaining some understanding about the behavior of this functional oxide, the synthesis environment and aging temperature were varied, and their affects were carefully analyzed using various materials analysis techniques such as high resolution transmission electron microscopy (HRTEM), UV-Visible spectroscopy (UV-Vis), and X-ray photoelectron spectroscopy (XPS). When the CNPs were aged at room temperature in as-synthesized condition, they were observed to spontaneously assemble and evolve as fractal superoctahedral structures. The reasons for this unique polycrystalline morphology were attributed to the symmetry driven assembly of the individual truncated octahedral and octahedral seed of the ceria. HRTEM and Fast Fourier Transform (FFT) analyses were used to explain the agglomeration behavior and evolution of the octahedral morphology. Some of the observations were supported by molecular dynamic simulations. Poly (ethylene glycol) (PEG) and ethylene glycol (EG) were used to control the kinetics of this morphology evolution. The ability to control the agglomeration of CNPs in these media stems from the lower dielectric constant and an increased viscosity of the EG and PEG based solvents. CNPs when synthesized and aged in frozen conditions, i.e. in ice, were found to form one dimensional, high aspect ratio structures. A careful analysis has provided some evidence that the CNPs use the porous channels in ice as a template and undergo oriented attachment to form nanorods. When the aging treatment was done near freezing temperature in solution, the nanorods were not observed, confirming the role of channels in ice. When synthesized in aqueous media such as DI water, PEG and EG; CNPs were observed to exhibit a reversible oxidation state switching between +3 and +4. Band gap values were computed from the optical absorption data. The changes in the band gap values observed were attributed to the changes in the oxidation state of CNPs as opposed to the quantum confinement effects, as expected in other nanoparticle systems. The work presented in this dissertation demonstrates, with evidence, that in order to obtain a comprehensive understanding of the properties of nanoscale materials it is of paramount importance to monitor their behavior over relatively longer periods of time under various ambient environments. While the solution based techniques offer a versatility and low cost route to study the fundamental properties of nanomaterials, they suffer some inherent problems such as precursor contamination and uncontrolled chemical reactions. Especially when analyzing the behavior of ceria-based materials for applications like solid oxide fuel cells, a great control in the density and crystalline quality are desired. In order to achieve this, as a first step pure ceria thin films were synthesized using oxygen plasma assisted molecular beam epitaxy (OPA-MBE). The ceria films were analyzed using various in situ and ex situ techniques to study the crystal structure, growth mode and epitaxial quality of the films. It was observed that the epitaxial orientation of the ceria films could be tuned by varying the deposition rate. When the films were grown at low deposition rate ([less than]8 [angstrom]/min) ceria films with epitaxial (200) orientation were observed where as the films grown at high deposition rates (up to 30 [angstrom]/min) showed (111) orientation. Theoretical simulations were used to confirm some of the experimental facts observed in both nanoparticles and thin films.