We have recently developed a hierarchical equations-of-motion (HEOM) approach to nonperturbative and non-Markovian quantum dissipation. It is a unified and exact theory for arbitrary coupling Gaussian environments of distinct nature: bosonic versus fermionic, and canonical versus grand canonical ensembles. It admits also an arbitrary time-dependent external field driving. Two systems will be used to elaborate both the formulation and implementation aspects of the theory. In an electron transfer (ET) system, the bath environment serves as a canonical bosonic ensemble, responsible for the system decoherence and energy relaxation. The validation of Zusman equation will be discussed, on the basis of exact HEOM results. In a quantum transport setup, a molecule or quantum dot is placed in contact with electrodes under applied voltage. Each electrode reservoir serves as a grand canonical fermion ensemble. It is responsible not only for decoherence and energy relaxation, but also for the fermion particle (i.e., electron) transport in/out of the system. The HEOM-based quantum transport theory will be summarized, together with the calculated transient currents through model quantum dot systems and the current spectrums in response to various forms of external time-dependent applied voltage. Support from RGC of Hong Kong Government is acknowledged. R.X. Xu and Y. J. Yan, Phys. Rev. E, 75, 031107 (2007). J. S. Jin, X. Zheng, and Y. J. Yan, J. Chem. Phys. 128, 234703 (2008). X. Zheng, J. S. Jin, and Y. J. Yan, J. Chem. Phys. 129, 184112 (2008). X. Zheng, J. S. Jin, and Y. J. Yan, New J. Phys. 10, 093016 (2008).