Nanofluidic devices are known to exhibit a plethora of non-equilibrium ion transport phenomena due to the presence of surface charge on domains comparable in size to the Debye length. With the help of asymptotic analyses and numerical simulations, we shed light on the physical mechanisms of nanofluidic devices like batteries and diodes, and designed new nanofluidic devices like inductors and oscillators. Nanofluidic batteries are energy generating systems for converting mechanical work into electrical power. An atomically smooth surface can reduce the drag of a flow by relaxing the no-slip boundary condition with a slip length. We found finite optimum values of surface charge density and ionic strength for specific slip lengths to design a more efficient nanofluidic battery. As simple as it may seem, conic-shaped nanopores can be used to design non-equilibrium devices such as diodes and inductors. For these nanopores, we observed current rectification such that the ion current is asymmetric with respect to the voltage polarization. More intriguingly, under DC bias at low frequency, the AC impedance of the conic nanopore behaved like a serial RL circuit with positive bias and a parallel RC circuit with reverse bias. By expanding from the weakly ion selective limit of a cross-section averaged model, we were able to derive explicit analytical solutions to quantitatively capture empirical and numerical data for ion current rectification and AC impedance data. Another interesting non-equilibrium device, an oscillator, was designed by coupling pressure-driven flow with history dependent electroosmotic flow. Autonomous current and mass flow oscillations were produced in an ion-selective monolith based on the hysteretic conductance of a wetting film around an expanding/contracting air bubble. A regular oscillation of ion current was sustained indefinitely under a DC voltage. Nanofluidic systems that exhibit electricity generation, current rectification, inductance and oscillations have hence all been developed and verified by careful analyses of the underlying non-equilibrium phenomena. These non-equilibrium systems are very sensitive to surface charge. Since biomolecules carry inherent charges and hence introduce new surface charges when they are within these nanofluidic devices, the next step is to utilize these systems to develop an efficient multiplex biosensing platform.