This review is devoted to a new object in nonlinear physics--Rossby solitons. The following questions are examined in greatest detail: 1) experimental observation of Rossby solitons in the laboratory; the geometric and kinematic properties, stability, collisions, and methods of generation of Rossby solitons; 2) self-organization of a Rossby autosoliton in unstable oppositely directed (zonal) flows; 3) a stationary laboratory model of natural vortices of the Jovian Great Red Spot (JGRS) type based on the Rossby autosoliton; 4) the question of the uniqueness of the JGRS along the perimeter of the planet; and 5) paired Rossby vortices. The theory and experiment are compared. The analogy between Rossby vortices and drift vortices in a plasma is pointed out.