Studies are reviewed on the development and application of a new method of measuring the magnetic susceptibility of single biological cells and liposomal bilayer aggregates that model the core of the cell membrane, and also any nonmagnetic and weakly magnetic microparticles of volume of the order of 10$^{-10}$ cm$^3$, without violating their integrity. The method is based on the phenomenon of magnetophoretic motion of cells in a buffer medium caused by the interaction of the magnetic moment of the cell induced by an external magnetic field with the fringing field of a thin magnetic filament magnetized by the same field. It enables measuring induced moments of either sign of the order of 10$^4$--10$^5$ Bohr magnetons in a field of 1 kOe. The potentialities of the method are illustrated by the results of studies of the magnetic properties of human erythrocytes containing hemoglobin in the fundamental forms obtained as functions of the temperature, the pH of the medium, and oxygen-exchange processes. The properties of hemoglobin in cells and solutions are compared. The possibility is noted of identifying the magnetic properties and the physiological state of the cells. By using magnetic capture of spherical and cylindrical multilayer liposomes, one can obtain the most complete information on the magnetic properties of the lipid bilayer--its magnetic susceptibility, diamagnetic anisotropy, and the components of the magnetic susceptibility tensor. These potentialities of magnetic capture have been realized experimentally, and by using it new information has been obtained on the features of the thermotropic behavior of membrane bilayers of synthetic dipalmitoyllecithin in the region of the fundamental phase transition and of bilayers of natural phospholipids–egg lecithin and the total lipids of erythrocyte membranes in the region of thermal structural rearrangements. The high sensitivity of magnetic capture to a change of the state of the lipid bilayer and its information content with respect to structural organization are noted.