Since 1995, more than 150 extrasolar planets were detected, of which a considerable fraction orbit their host star at very close distances. Gas giants with orbital distances below 0.1 AU are called “Hot Jupiters”. Current detection techniques are not sensitive enough for the detection of Earth-like planets, but such planets are expected at similar orbital positions. For all these so-called close-in extrasolar planets, the interaction between the stellar wind and the planetary magnetosphere is expected to be very different from the situation known from the solar system. Important differences arising from the close substellar distances include a low stellar wind velocity, a high stellar wind density and strong tidal interaction between the planet and the star. This interaction is shown to lead, for example, to a synchronisation of the planetary rotation with its orbit (“tidal locking”). Taking these points into account, planetary magnetic moments are estimated and sizes of planetary magnetospheres are derived. Two different effects resulting from the magnetospheric interaction are studied in detail. (a) Characteristics of radio emission from the magnetospheres of “Hot Jupiters” are discussed. It is shown that the frequency range and the sensitivity of current radio detectors are not sufficient to detect exoplanetary radio emission. With planned improvements of the existing instrumentation and with the construction of new radio arrays, the detection of exoplanetary radio emission will be possible in the near future. (b) The flux of galactic cosmic rays to the atmospheres of terrestrial exoplanets in close orbits around M stars is studied. Different types of planets are shown to be weakly protected against cosmic rays, which is likely to have implications for planetary habitability. This should be taken into account when selecting targets for the search for biosignatures in the spectra of terrestrial exoplanets.