The theory and empirical data for three classes of ocean eddies are summarized: 1) gigantic anticyclonic gyres; 2) meanders, rings, and synoptic eddies in the open ocean; and, 3) mesoscale eddies (lenses of foreign waters and rotating cells of forced convection). A number of new results obtained in the last few years are reported: linear and nonlinear instability of gigantic gyres, the Hamiltonian formalism for Rossby--Blinova waves, an eddy-resolving model of global ocean circulation, the discovery of deep mesoscale lenses of foreign waters, and the general prevalence of rotating cells of forced convection in the upper layer of the ocean.