The architecture of exoplanetary systems is often different from the solar system, with some exoplanets being in close orbits around their host stars and having orbital periods of only a few days. In analogy to interactions between stars in close binary systems, one may expect interactions between the star and the exoplanet as well. From theoretical considerations, effects on the host star through tidal and magnetic interaction with the exoplanet are possible; for the exoplanet, some interesting implications are the evaporation of the planetary atmosphere and potential effects on the planetary magnetism. In this review, several possible interaction pathways and their observational prospects and existing evidence are discussed. A particular emphasis is put on observational opportunities for these kinds of effects in the high-energy regime.