This paper deals with the problems encountered in the study of eukaryotic cell membranes. A discussion on the structure and composition of membranes, lateral heterogeneity of membranes, lipid raft formation, and involvement of actin and cytoskeleton networks in the maintenance of membrane structure is included. Modern methods for the study of membranes and their constituent domains are discussed. Various simplified models of biomembranes and lipid rafts are presented. Computer modelling is considered as one of the most important methods. This is stated that from the study of the plasma membrane structure, it is desirable to proceed to the diverse membranes of all organelles of the cell. The qualitative composition and molar content of individual classes of polar lipids, free sterols and proteins in each of these membranes must be considered. A program to create an open access electronic database including results obtained from the membrane modelling of individual cell organelles and the key sites of the membranes, as well as models of individual molecules composing the membranes, has been proposed.