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The hierarchical stochastic Schr?dinger equations(HSSE)are a kind of numerically exact wavefunction-based approaches suitable for the quantum dynamics simulations in a relatively large system coupled to a bosonic bath.Starting from the influence-functional description of open quantum systems,this review outlines the general theoretical framework of HSSEs and their concrete forms in different situations.The applicability and efficiency of HSSEs are exemplified by the simulations of ultrafast excitation energy transfer processes in large-scale systems.