The necessary conditions for producing lightning discharges, the experimental possibilities for investigating extraterrestrial lightning, and the scientific objectives of planetary lightning research are briefly discussed. Present knowledge on the composition, structure, and dynamics of the atmospheres for the extraterrestrial planets and the satellites Io and Titan are reviewed in terms of their importance for the production of lightning. From the knowledge on planetary atmospheres, intensive lightning activity can be expected to exist in the Jupiter and Saturn cloud systems; this is less conclusive for Venus and unlikely for the other bodies. Electrical activity is not completely ruled out for Martian dust storms. Optical and RF wave measurements from spacecraft have yielded evidence of possible lightning activity on Venus, Jupiter, and Saturn. These observations are reviewed and discussed. The conclusion that the optical and/or RF emissions are definitely from lightning is not unambiguous and based on poor data bases. There are no coincidence measurements of optical and RF pulses, and there is no information on the characteristics of individual pulses, which would help to clarify the source.