The near-atomic thickness and organic molecular systems, including organic semiconductors and polymer-enabled hybrid heterostructures, of two-dimensional transition metal dichalcogenides (2D-TMDs) can modulate their optoelectronic and transport properties outstandingly. In this review, the current understanding and mechanism of the most recent and significant breakthrough of novel interlayer exciton emission and its modulation by harnessing the band energy alignment between TMDs and organic semiconductors in a TMD/organic (TMDO) hybrid heterostructure are demonstrated. The review encompasses up-to-date device demonstrations, including field-effect transistors, detectors, phototransistors, and photo-switchable superlattices. An exploration of distinct traits in 2D-TMDs and organic semiconductors delves into the applications of TMDO hybrid heterostructures. This review provides insights into the synthesis of 2D-TMDs and organic layers, covering fabrication techniques and challenges. Band bending and charge transfer via band energy alignment are explored from both structural and molecular orbital perspectives. The progress in emission modulation, including charge transfer, energy transfer, doping, defect healing, and phase engineering, is presented. The recent advancements in 2D-TMDO-based optoelectronic synaptic devices, including various 2D-TMDs and organic materials for neuromorphic applications are discussed. The section assesses their compatibility for synaptic devices, revisits the operating principles, and highlights the recent device demonstrations. Existing challenges and potential solutions are discussed. Finally, the review concludes by outlining the current challenges that span from synthesis intricacies to device applications, and by offering an outlook on the evolving field of emerging TMDO heterostructures.