Semiconductor materials (e.g., conjugated polymers, metal halide perovskites) have been widely used in solar cells, light-emitting diodes, and photodetectors. Organic conjugated systems have high mechanical flexibility and low costs for production. Metal halide perovskites have the advantage of strong light absorption, long charge-carrier diffusion lengths, and low intrinsic surface recombination. Polarization-sensitive single-molecule methods have been extensively used to study the chromophore organization and excitation energy transfer (EET) process. Our novel polarization technique, two-dimensional polarization imaging (2D POLIM) is designed to simultaneously measure and control both the excitation and emission polarization characteristics of an individual object. A model based on single funnel approximation (SFA) is applied to fit the 2D polarization portrait obtained from 2D POLIM measurements. 2D POLIM in combination with the SFA model allows the quantitative characterization of EET efficiency. Overall, A large number of polarization parameters, e.g., modulation depths, phases, luminescence shift, fluorescence anisotropy, energy funneling efficiency, and properties of the EET-emitter, can be extracted from 2D polarization portraits. They give a full picture of chromophores' organization and a quantitative measure of the EET process. In this thesis, we applied the 2D POLIM technique to investigate the fundamental optoelectronic process in different types of luminescent materials. H-aggregates forming in spin-cast conjugated films are visualized by modulation depth and phase imaging contrast. Light-harvesting efficiency shows the efficient ET within the amorphous phase and poor ET between H-aggregates due to the less overlap between absorption and emission spectra. Together with single-molecule spectroscopy and scanning electron microscope, we studied the polarization property of individual MAPbBr3 aggregates, which shows the well-known dielectric screening effect cannot fully explain the absorption polarization from weakly elongated objects (even with irregular shapes). We propose that power dependent quantum yield can further increase the modulation depth of excitation. 2D POLIM was also applied to explore the aggregation state of proteins in the biological system. Furthermore, we did a series of computer experiments to examine and improve the SFA model. We break the limit of energy funneling efficiency and propose an asymmetric three-dipole model, which is more applicable for multi-chromophore systems. In the future, quantitative phase-contrast imaging and time-resolved 2D POLIM might be further developed.