Structurally defined nanopores have received great attention in the past decades in part due to the novel mass transport phenomena resolved at such nanoscale solid-liquid interfaces. New capabilities and/or better efficiency are envisioned in molecular sensing, energy storage and conversion, nanofluidics, and membrane transport. This review will focus on the fundamental mass transport processes confined by asymmetric nanoscale structures particularly in conical nanopores. The fabrication of different nanopore devices and the double layer theory are briefly introduced first as background. The nonlinear and dynamic mass transport processes, including ionic current rectification, dynamic concentration polarization, memory effects and capacitive charging/discharging processes are then reviewed. The fundamental understanding and quantification of dynamic transport features offer new physical insights in the nanoscale mass transport processes and has significant implications in related electroanalytical and other applications. (C) 2016 Elsevier B.V. All rights reserved.