Perturbations vary in period and amplitude, and responses to unavoidable perturbations depend on response time and scale. Disturbances due to unavoidable perturbations occur in three translational planes and three rotational axes during forwards and backwards swimming. Stability depends on hydrodynamic damping and correcting forces, which may be generated by propulsors (powered) or by control surfaces moving with the body (trimming). Hydrostatic forces affecting body orientation (posture) result in negative metacentric heights amplifying rolling disturbances. The ability to counteract perturbations and correct disturbances is greater for fishes with more slender bodies, which appears to affect habitat choices. Postural control problems are greatest at low speeds, and are avoided by some fishes by sitting on the bottom. In currents, body form and behavior affect lift, drag, weight, and friction and hence speeds to which posture can be controlled. Self-correcting and regulated damping and trimming mechanisms are most important in stabilizing swimming trajectories. Body resistance, fin trajectory, multiple propulsors, and long-based fins damp self-generated locomotor disturbances. Powered control using the tail evolved early in chordates, and is retained by most groups, although fishes, especially acanthopterygians, make greater use of appendages. As with most areas of stability, little is known of control costs. Costs and benefits of low-density inclusions and hydrodynamic mechanisms for depth control vary with habits and habitats. Control may make substantial contributions to energy budgets.