Micropumping is difficult to design and control as compared to their macro-scale counterparts due to the size limitation. The first part of this dissertation focuses on micropumping with surface tension forces. A simple, single-action, capillary pump/valve consisting of a bi-phase slug confined in a non-uniform conduit is described. At low temperatures, the slug is solid and seals the conduit. Once heated above its melting temperature, the liquid slug moves spontaneously along a predetermined path due to surface tension forces imbalance. This technique can be easily combined with other propulsion mechanisms such as pressure and magnetohydrodynamics (MHD). The second part of this dissertation focuses on MHD micropumping, which provides a convenient, programmable means for propelling liquids and controlling fluid flow without a need for mechanical pumps and valves. Firstly, we examined the response of a model one dimensional electrochemical thin film to time-independent and time-dependent applied polarizations, using the Nernst-Planck (NP) model with electroneutrality and the Poisson-Nernst-Planck (PNP) model without electro -neutrality, respectively. The NP model with well designed boundary conditions was v developed, proved capable of describing the bulk behavior as accurate as the full PNP model. Secondly, we studied the MHD propelled liquid motion in a uniform conduit patterned with cylinders. We proved equivalence in MHD and pressure driven flow patterns under certain conditions. We examined the effect of interior obstacles on the electric current flow in the conduit and showed the existence of particular pillar geometry that maximizes the current. Thirdly, we looked at MHD flow of a binary electrolyte between concentric cylinders. The base flow was similar to the pressure driven flow in the same setup. The first order perturbation fields, however, behave differently as the traditional Dean’s flow. We carried out one-dimensional linear stability analysis for the unbounded small gap situation and solved it as an eigenvalue problem. Two-dimensional nonlinear simulation was performed for finite gap size or bounded situations. We observed strong directionality of the applied electric field for the onset of stability. Results in this study could help enhance the stability of the system or introduce secondary motion depending on the nature of the applications.