Parametric instabilities, excited in the ionosphere by high-power HF transmitters with a frequency below the maximum ionospheric plasma frequency, produce nonlinear energy absorption and enhanced scattering of electromagnetic radiation, which has been detected by the Arecibo Thomson scatter radar. This paper reviews and extends both the linear and nonlinear saturation theory of parametric instabilities within the ionospheric context. The new elements are a modification of the emission term to include the effects of nonlinear plasma waves and a numerical integration of the wave kinetic equation to find the saturation state of parametric instabilities when it is assumed only that the wave intensity has axial symmetry about the pump field in wave number space. Calculations are presented of the magnitude of the nonlinear energy absorption and of the angular dependence, frequency spectrum, and intensity of scattering from instability-created density fluctuations. In the present experiments the nonlinear processes are predicted to absorb roughly 30% of the radio wave energy incident on the ionosphere. As a rule, this energy is deposited in the high-energy tail of the electron velocity distribution and causes enhanced airglow. The scattered radiation has a frequency shift almost equal to the modifier frequency, and its intensity depends strongly on the angle between k and E0, k being the wave vector of the plasma wave responsible for the scattering and E0 the pumping electric field produced by the modification transmitter. Because the instabilities occur only with O mode transmissions, the direction of E0 is close to the geomagnetic field. The angular dependence result rests on a combination of two-dimensional saturation calculations and plasma wave refraction due to propagation in the inhomogeneous magnetoactive ionospheric plasma. For example, the plasma waves responsible for the scattering observed at Arecibo are found to be nonlinearly stabilized and roughly 104 times less intense than plasma waves propagating within 20° of the geomagnetic field. Thus the scattering observed at Arecibo, although it is intense by Thomson scatter standards, is predicted to be ∼40 dB below the scattering observable in the most favorable geometry. Lastly, new aeronomy experiments made possible by parametric instabilities are discussed.