Nanofibrous membranes generated by the electrospinning technique possess several unique structural properties, such as high surface and bulk porosity, high surface-to-volume ratio and interconnected pores, and have attracted considerable attention in the past two decades. For many of the membrane applications, such as tissue engineering and water filtration, the pore size and its distribution are important parameters. A better understanding of the relationships between the pore size, membrane thickness, fiber diameter and porosity is crucial for tailoring such membranes for specific applications. Capillary flow porometry was used to study the pore size, and quantitative relationships between the mean flow pore size and other structure properties can be obtained. The design and characterization of nanofibrous membranes with specific properties, as well as the exploration of their potential applications represent another part of the dissertation. In the nanofibrous membrane application to microfiltration, electrospun membranes with different pore sizes were evaluated for their performance in removing water-borne bacteria by using spherical particles with different sizes as the simulants. Another issue deals with the bonding between the nanofibrous membrane and its non-woven substrate which often requires further strengthening for many practical applications in the ultrafiltration and nanofiltration range. A simple hot-pressing method combined with an interfacial treatment has been tried to improve the bonding between the support and the electrospun layer. The further modified structure could provide better mechanical support when used as the scaffold of the UF/NF membranes to withstand backflushing. The electrospun nanofibrous membrane also demonstrated its application to the lithium-ion battery. By depositing the electrospun polyethersulfone membrane onto the chemically treated commercial polyethylene microporous separator, the thermal property and the safety margin of such a separator could be greatly improved, without sacrificing other properties of the separator. A simple method of preparing the efficient and cost-effective electrospun nanofibrous microfiltration membranes with hazard chromium (VI) removal ability was presented. A functional material with a high positive charge density was grafted onto the nanofibers. The resulting membrane demonstrated both superior Cr(VI) adsorption capacity to the commercial activated carbons and reusability after proper treatment.