  A number of non-Markovian stochastic Schr\"odinger equations, ranging from
the numerically exact hierarchical form towards a series of perturbative
expressions sequentially presented in an ascending degrees of approximations
are revisited in this short review, aiming at providing a systematic framework
which is capable to connect different kinds of the wavefunction-based
approaches for an open system coupled to the harmonic bath. One can
optimistically expect the extensive future applications of those non-Markovian
stochastic Schr\"odinger equations in large-scale realistic complex systems,
benefiting from their favorable scaling with respect to the system size, the
stochastic nature which is extremely suitable for parallel computing, and many
other distinctive advantages. In addition, we have presented a few examples
showing the excitation energy transfer in Fenna-Matthews-Olson complex, a
quantitative measure of decoherence timescale of hot exciton, and the study of
quantum interference effects upon the singlet fission processes in organic
materials, since a deep understanding of both mechanisms is very important to
explore the underlying microscopic processes and to provide novel design
principles for highly efficient organic photovoltaics.
