Membranes are asymmetric sheet like enclosed structures with an inside and an outside. These sheet like structures are thermodynamically stable but electrically and metabolically active. By forming closed compartments around cellular protoplasm, membranes separate one cell from another, thus permitting cellular individuality. Membranes act as barrier, with selective permeabilities to material and information. Classical “sandwich model” for membranes was proposed by Daniel Li and Davson as a result of indirect experiments of surface tension and thickness estimates of membrane. Singer and Nicolson modified sandwich and unit membrane model and proposed fluid mosaic model to explain dynamic structure and fluidity of membranes. Noteworthy features of these models have been highlighted. Information on gates and pumps of membranes along with its electrical properties such as capacitance, resistance and conductance has been provided in this chapter. Various transport processes such as diffusion, primary, secondary, and gradient coupled active transport, endocytosis, exocytosis, proton mediated and anti biotic mediated transports across the membrane have been given in the text. Role of transmission and freeze fracture electron microscopy, sonification, nuclear magnetic resonance and X-ray diffraction techniques for the study of structure and functions of biological and artificial membranes have been summarized in the text.