Multiphase microfluidics offers a great number of opportunities in different applications ranging from analytical chemistry, chemical engineering, pharmaceutical and biomedical sciences, to life science. The present work builds models of flow fields in liquid plugs moving in microchannels, and implements these models to investigate the transport phenomena in multiphase microfluidics. To understand the flow fields within liquid plugs in microchannels, four models of flow fields are developed for plugs in different channel geometries, such as microcapillaries/microchannels with circular cross section, two-dimensional microchannels, curved microchannels, and plug trains in two-dimensional microchannels. These models offer conveniences for subsequent analyses since transport phenomena can be analyzed directly with the known flow fields. Different applications are demonstrated with the proposed models, such as the flow resistance, the heat transfer in plugs, and the chaotic mixing in plugs moving in meandering microchannels. Based on the results provided by the model, some ideas are proved to utilize and to manipulate multiphase microfluidics. A method to split droplets mediated by hydrodynamic focusing is proposed and investigated. The number and the size of the daughter droplets are controllable by varying the splitting flow rate and the size of the mother droplet. This method of droplet splitting is proved robust, reliable, and flexible. The studies of liquids and gas-liquid plugs at the outlet of microcapillaries are performed. For a liquid, it leaves a capillary in the form of pendant drop. During the growth and breakup of pendant drops, with a fixed flow rate at the inlet of the capillary, upstream pressure fluctuation is produced by the size variation of the pendant drop. The pressure fluctuation can be used to measure the surface tension of the fluid by measuring the period of the pressure fluctuation. For gas/liquid plug flow, fluids leave a microcapillary in the form of compound pendant drops. With a fixed upstream pressure, velocity fluctuation in the upstream is caused by the formation and breakup of compound pendant drops. Experimental investigation shows that the velocity fluctuation is reduced by adding surfactant into the liquid. DOCTOR OF PHILOSOPHY (MAE)