Magnetic reconnection is a basic process taking place in plasmas on Earth and in space. After a general introduction, this work focusses on magnetic reconnection in the Earth' magnetosphere. Because of the interaction between the solar wind and the terrestrial magnetic field, magnetic field line merging is initiated under certain conditions, leading to various phenomena like the polar aurora or the injection of high-energetic particles influencing near-Earth satellites. The author presents a method to achieve detailed information about the reconnection process from remote satellite measurements. Therefore, an ill- posed inverse problem is solved using regularization theory. Using multi-spacecraft measurements, e.g. from the Cluster satellites, it is possible to gain information about the spatial location of the reconnection event, so this method presents a complementary approach to ground-based and in-situ satellite measurements. The work combines a thorough analysis of theoretical space plasma problems with experimental data from satellite missions and numerical simulations to provide new insights in this exciting field of space physics.