The development of new materials and electronic devices which exhibit unique physical properties will allow for the next technological leap toward brain-inspired computing. Among all functional materials, vanadium oxides such as VO2 and V2O3 are at the forefront of condensed matter physics/materials science research and are considered promising candidates for memory and computing applications. These oxides are well-known Mott insulators that feature metal-insulator transitions (MITs) and resistive switching (RS). In response to temperature, electric field, or other external stimuli, a significant change in electrical resistivity can be observed during the phase transition. Neuronal or synaptic functionalities could be thus implemented using these properties, which serve as the fundamental building blocks for neuromorphic technologies. Despite this interest, the underlying physical mechanisms responsible for these phenomena are still not clear. The aim of this dissertation is to investigate and understand the MITs and RS behavior in different vanadium oxides using novel synthesis/characterization methods. To begin with, this dissertation discusses a high-vacuum gas evolution technique, in which the oxygen partial pressure and temperature can be precisely adjusted to strategically control the oxygen stoichiometry in vanadium oxide thin films. Using this technique, we successfully stabilized the V3O5 exotic phase despite its extremely narrow phase stability range. In addition, we were able to control the phase transformation between VO2, V3O5, and V2O3, and ultimately manipulate the MITs between different phases. Furthermore, the electrically induced resistive switching effects of these strongly correlated oxides and the applications of neuromorphic computing devices will be discussed. A joint study of ex-situ electrical transport measurements and in-situ characterization techniques was carried out to investigate the volatile and non-volatile resistive switching mechanisms. We demonstrated that vanadium oxide-based switching devices can exhibit both neuron-like or synapse-like functionalities under electric stimuli. Our work presents a comprehensive investigation of new material/technique development, fundamental physical mechanisms, and electronic device applications. We believe our findings can help pave the way for the development of next-generation computing technologies.