Structurally defined nanopores have received great attentions in the past decade for both novel mass transport phenomena at nanoscale solid-liquid interfaces and practical applications exploiting such processes. New capabilities and/or better efficiency are envisioned in molecular sensing, energy storage and conversion, nanofluidics, and membrane transport. However, the dynamics of the mass transport (MT) processes in nanopores remain poorly understood, albeit steady-state MT processes have been extensively studied. In this dissertation, multiple time and frequency- domain electrochemical techniques have been used in combination with simulation to investigate the dynamic transport of aqueous electrolytes through single conical nanopore embedded in glass membrane or capillary. Electrical ionic current results from the transport of ions or other charged species. The current signal is limited by and thus reflects the transport at the most resistive/smallest nanopore region. Stimulated by an external triangular potential waveform, an intriguing non-zero cross point and pinched hysteresis current-potential curves have been discovered. Those emerging transport behaviors are quantified and correlated to the surface and geometry properties of the nanopores as well as the frequency of the external stimuli. Accordingly, multiple processes with different transport dynamics are deconvoluted and quantified respectively. At different frequency ranges, the dynamics of concentration polarization and ionic current rectification are decoupled from the charging/discharging of the glass membrane. Furthermore, physical models and empirical equations are proposed to describe the nonlinear current-potential responses. The last chapter of this dissertation describes the electronic structures and corresponding physicochemical properties of gold-thiolate clusters as novel functional nanomolecules.