Turbulent flows and turbulent flames are inherently multi-dimensional in space and transient in time. Therefore, multidimensional diagnostics that are capable of resolving such spatial and temporal dynamics have long been desired; and the purpose of this dissertation is to investigate three such diagnostics both for the fundamental study of flow and combustion processes and also for the applied research of practical devices. These multidimensional optical diagnostics are a 2D (two dimensional) two-photon laser-induced fluorescence (TPLIF) technique, a 3D hyperspectral tomography (HT) technique, and a 4D tomographic chemiluminescence (TC) technique. The first TPLIF technique is targeted at measuring temporally-resolved 2D distribution of fluorescent radicals, the second HT technique is targeted at measuring temperature and chemical species concentration at high speed, and the third TC technique is targeted at measuring turbulent flame properties. This dissertation describes the numerical and experimental evaluation of these techniques to demonstrate their capabilities and understand their limitations. The specific aspects investigated include spatial resolution, temporal resolution, and tomographic inversion algorithms. It is expected that the results obtained in this dissertation to lay the groundwork for their further development and expanded application in the study of turbulent flow and combustion processes.