Among the Solar-type stars observed in the Galaxy, many appear to be metal-rich relative to the Sun. The case of exoplanet-host stars is particularly interesting in that respect since they present, on average, an overmetallicity of 0.2 dex. This metallicity is probably original, from the protostellar nebula, but it could also have been increased by accretion of hydrogen-poor material during the early stage of planetary formation. Asteroseismic studies provide an excellent way to determine the internal structure and chemical composition of these stars. Such studies may also establish constraints on the external parameters (gravity, effective temperature, metallicity) that are more precise than the constraints obtained from spectroscopy. After a general discussion on this subject, I present the special cases of three stars: µ-Arae, which was observed with the HARPS spectrograph in June 2004; ι-Horologii, which has been modeled in detail and will be observed with HARPS in November 2006; and finally HD 52265, one of the main targets of the COROT mission, an exoplanet-host star that will be observed with the COROT satellite for five consecutive months.