Singlet fission is a photophysical process in organic materials where a photoexcited singlet exciton splits into two triplet excitons. This process has gained a lot of interest in the past decade for enhancing the efficiency of photovoltaic conversion. Precious work identified a crucial intermediate state in singlet fission, and the construction of the wave function for this correlated triplet-pair state poses a significant challenge. This article serves as a comprehensive introduction to theoretical models designed for constructing the wave function of the correlated triplet-pair. Subsequently, we delve into an exploration of the intricate effects of vibrational, orbital, and spin interactions on the formation and dissociation of the intermediate state. Finally, we conclude with a succinct summary of the challenges anticipated to shape the landscape of future theoretical research in this field.