Abstract: Over the past decades, transport models have achieved remarkable success in revealing nuclear reaction mechanisms within this energy range. As research progresses, there is growing demand for transport models with higher predictive accuracy. This article briefly introduces the BBGKY hierarchy equations and their truncation, emphasizing that two-body correlations and their induced fluctuation effects constitute two critical aspects requiring consideration for advancing heavy-ion transport models in the low-to-intermediate energy regime. We review progress in correlation and fluctuation studies through three categories of transport models: quantum Boltzmann equation-based approaches, time-dependent density matrix formulations, and quantum molecular dynamics frameworks. The primary objectives are to clarify interrelationships among these models and propose development directions for next-generation heavy-ion transport models in intermediate energy domains.