Over the last 25 years one of us (WKS) has been investigating physical properties of lipid bilayer membranes. In 1991 a group led by WKS was organized into the Laboratory of Structure and Dynamics of Biological Membranes, the effective member of which is AW. Using mainly the electron paramagnetic resonance (EPR) spin-labeling method, we obtained unexpected results, which are significant for the better understanding of the functioning of biological membranes. We have developed a new pulse EPR spin-labeling method for the detection of membrane domains and evaluation of lipid exchange rates. This review will be focused on our main results which can be summarized as follows: (1) Unsaturation of alkyl chains greatly reduces the ordering and rigidifying effects of cholesterol although the unsaturation alone gives only minor fluidizing effects, as observed by order and reorientational motion, and rather significant rigidifying effects, as observed by translational motion of probe molecules; (2) Abbreviations: EPR, electron paramagnetic resonance; PC, phosphatidylcholine; DXPC (where X = L, M, P, S, B, O, E), dilauroyl-, dimyristoyl-, dipalmitoyl-, distearoyl-, dibehenoyl-, dioleoyl-, dielaidoylphosphatidylcholine, respectively; EYPC, egg-yolk phosphatidylcholine; POPC, 1-palmitoyl-2-oleoylphosphatidylcholine; BR, bacteriorhodopsin; IFV, influenza virus; SASL, stearic acid spin label; 16-SASL, 16-doxylstearic acid spin label; SLOT domain, slow oxygen transport domain; DOT method, method of discrimination by oxygen transport; T 1, spin-lattice relaxation time.Here, the word "transport" is used in its basic physical sense indicating the product of the (local) translational diffusion coefficient and the (local) concentration of oxygen in the membrane.