  Magnetic interactions between a planet and its environment are known to lead
to phenomena such as aurorae and shocks in the solar system. The large number
of close-in exoplanets that were discovered triggered a renewed interest in
magnetic interactions in star-planet systems. Multiple other magnetic effects
were then unveiled, such as planet inflation or heating, planet migration,
planetary material escape, and even modification of the host star properties.
We review here the recent efforts in modelling and understanding magnetic
interactions between stars and planets in the context of compact systems. We
first provide simple estimates of the effects of magnetic interactions and then
detail analytical and numerical models for different representative scenarii.
We finally lay out a series of future developments that are needed today to
better understand and constrain these fascinating interactions.
