Electrical impedance imaging technology, an emerging damage monitoring technique, is deemed highly promising in aerospace structural health monitoring, owing to its non-invasive nature, rapid response, and simple equipment setup. This article first reviews the developmental history of electrical impedance tomography algorithms and summarizes the significant achievements made in recent years, both domestically and internationally, in forward problem modeling, regularization, and inverse problem solving. Then, a systematic summary was conducted on the damage monitoring applications of EIT technology for resin-based, ceramic-based, and other functional materials commonly used in the aerospace field. The existing feasible electrode array arrangements and excitation schemes for three-dimensional structures using EIT technology were also summarized. Finally, the existing technical problems of electrical impedance tomography technology were pointed out, and the future development direction was discussed.