The giant planets Jupiter and Saturn belong to the interesting category of possible goals for remote seismic analysis. Their first seismic observations and their analysis were attempted in 1987 and 1991 respectively, under Philippe Delache's initiative. The theoretical analysis of giant planets seismology reveals the strong signature of the dense planetary core and the tiny one of the hydrogen plasma phase transition. The asymptotic formalism makes possible to obtain pertinent information for the observation of planetary oscillations and for their analysis. Specific observational techniques were developed to detect the seismic signature of giant planets. However, the first observations (Schmider et al. 1991, Mosser et al. 1993) of Jovian oscillations remain tentative. Even if the Jovian origin of the signal is beyond doubt, the interpretation in terms of Jovian global modes remains speculative. The collision of comet SL9 onto Jupiter provided an unexpected and unique opportunity to search for oscillations excited by the cometary impacts (Mosser et al. 1996). Seismic observations of Saturn remain negative so far. Therefore, this review focuses on Jupiter. Finally, the almost 10-years long experience of seismic observations of Jupiter and Saturn has not yet provided new constraints for planetary interior models. However, guidelines for future observational projects dedicated to Jovian seismology can be drawn. The different techniques of observation are compared, and observational requirements are precisely described.