This issue contains a selection of 10 papers of the 15th International Workshop on Optimization and Inverse Problems in Electromagnetism (OIPE 2018). One focus of this edition of OIPE was theoretical aspects and fundamentals including the formulation of inverse problems and design problems, model order reduction, sensitivity analysis and regularization techniques. Emphasis was also put on novel optimization algorithms. Furthermore, applications in the fields of transportation, non-destructive evaluation, smart grids, electrical machines and biomedical engineering were presented. Finally, a special session within the program was devoted to the emerging field of computational electromagnetism.