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The advancements in our fundamental understanding of light-matter interaction in the past century are foundational to our technology-enabled modern lifestyle. While the physics and technology of inorganic semiconductors have been well-developed in the past 60 years, the development of organic semiconductors is in its nascent stages. Combination of the two material systems in organic-inorganic (OI) hybrid semiconductor systems have already found applications in next-generation solar cells, light-emitting diodes, and non-linear optical devices, yet the unique charge and exciton behavior at OI heterojunctions (HJs) remains largely unexplored. The stark differences in the optoelectronic properties of organic and inorganic semiconductors offer a rich and as of yet unexplored territory of charge and energy transfer processes in hybrid semiconductor systems. Expanding the physical understanding of these coupled material systems could potentially lead to major advances in semiconductor applications and science. This thesis presents the first steps toward developing a comprehensive understanding of charge and exciton dynamics in coupled hybrid OI material systems. A theory of optical and electrical behavior of OI-HJ based diodes is outlined. The theory yields a quantitative model for current density versus voltage (J-V) characteristics of OI-HJ based diodes. The existence of a hybrid charge transfer exciton (HCTE) state, composed of a columbically-bound electron in the inorganic semiconductor and hole polaron in the organic semiconductor, is predicted at the hybrid heterointerface. The HCTE is found to be the the fundamental quasi-particle that governs the excited state properties of the diode. A first principles quantum mechanical model of the HCTE is developed to predict its optoelectronic properties. The external quantum efficiency, electroluminescence, photoluminescence, and J-V characteristics for multiple OI diode systems are presented along with model fits to the data. The fits yield insights into the dominant optoelectronic processes in OI material systems, including trap-mediated charge recombination and space-charge-limited current. The ability to systematically manipulate the optoelectronic properties of the HCTE by tuning the dimensionality of electron delocalization in the inorganic semiconductor is demonstrated. Potential novel applications and future directions for exploration that emerge for hybrid material systems as a result of the findings of this thesis are also discussed.