Ion current rectification (ICR) refers to the asymmetric potential-dependent rate of the passage of solution ions through a nanopore, giving rise to electrical current-voltage characteristics that mimic those of a solid-state electrical diode. Since the discovery of ICR in quartz nanopipettes two decades ago, synthetic nanopores and nanochannels of various geometries, fabricated in membranes and on wafers, have been extensively investigated to understand fundamental aspects of ion transport in highly confined geometries. It is now generally accepted that ICR requires an asymmetric electrical double layer within the nanopore, producing an accumulation or depletion of charge-carrying ions at opposite voltage polarities. Our research groups have recently explored how the voltage-dependent ion distributions and ICR within nanopores can induce novel nanoscale flow phenomena that have applications in understanding ionics in porous materials used in energy storage devices, chemical sensing, and low-cost electrical pumping of fluids. In this Account, we review our most recent investigations on this topic, based on experiments using conical nanopores (10-300 nm tip opening) fabricated in thin glass, mica, and polymer membranes. Measurable fluid flow in nanopores can be induced either using external pressure forces, electrically via electroosmotic forces, or by a combination of these two forces. We demonstrate that pressure-driven flow can greatly alter the electrical properties of nanopores and, vice versa, that the nonlinear electrical properties of conical nanopores can impart novel and useful flow phenomena. Electroosmotic flow (EOF), which depends on the magnitude of the ion fluxes within the double layer of the nanopore, is strongly coupled to the accumulation/depletion of ions. Thus, the same underlying cause of ICR also leads to EOF rectification, i.e., unequal flows occurring for the same voltage but opposite polarities. EOF rectification can be used to electrically pump fluids with very precise control across membranes containing conical pores via the application of a symmetric sinusoidal voltage. The combination of pressure and asymmetric EOF can also provide a means to generate new nanopore electrical behaviors, including negative differential resistance (NDR), in which the current through a conical pore decreases with increasing driving force (applied voltage), similar to solid-state tunnel diodes. NDR results from a positive feedback mechanism between the ion distributions and EOF, yielding a true bistability in both fluid flow and electrical current at a critical applied voltage. Nanopore-based NDR is extremely sensitive to the surface charge near the nanopore opening, suggesting possible applications in chemical sensing.