The principle and the feasibility of dispersion compensators in planar photonic crystals based on the insulator-on-silicon-on-insulator (IOSOI, SiO2/Si/SiO2) system were demonstrated. This dispersion compensator should compensate for the dispersion of a single-wavelength channel with a bandwidth of 0.4 nm, corresponding to 40 GHz at 1.55 µm wavelength, and be integrated into a silicon chip, in order to be compatible with other electrical and optical integrated devices. Due to the small thickness of the silicon core and the high index contrast between the core and the oxide claddings, the behaviour of the IOSOI system is fully three-dimensional and combines the properties of a two-dimensional photonic crystal with those of a planar waveguide. Performing theoretical studies on the properties of this planar photonic crystal, a design of a dispersion compensator taking into account several requirements for a good device functionality was elaborated and optimized. Issues like the light confinement, the radiation losses and the existence of cladding modes were addressed, as well as their consequences on the device properties. Light coupling from an integrated ridge waveguide into the photonic crystal waveguide used as the dispersion compensator was also discussed. Though challenging, the experimental fabrication of such devices, compatible with the standard silicon technology, was demonstrated. Moreover, a theoretical estimate showed that the small experimental imperfections, arising from the process difficulties, may be compensated after fabrication by tuning via free-carrier injection.