This review is devoted to a systematic exposition of theoretical and experimental results related to the physics of cylindrical magnetic domains (bubbles). The stability problem is discussed for an individual cylindrical domain and for a lattice of such domains, with allowance for the effect of the coercivity on the stability and dynamics of cylindrical domains. A detailed discussion is given of the laws of motion of cylindrical magnetic domains under the influence of inhomogeneities of magnetic field, temperature, and plate thickness. Phase transitions in a lattice of domains are considered, and the singularities of the magnetization and magnetic susceptibility in such phase transitions are determined. A theory is given for waves propagated in a lattice of domains. Detailed consideration is given to the effect of external factors and of the parameters of the magnetic material on the dynamical properties of a lattice of domains.