This study focuses on students' conceptions of electric and magnetic fields at university level and of the interrelations between them. A total of 33 students participated in a paper and pencil test after the completion of first-year electricity and second-year electromagnetism courses. The conceptions were investigated in the contexts of a charged particle, a charging capacitor, electromagnetic induction, and an electromagnetic plane wave. The results show that students do not include the vector nature of field quantities in their reasoning. In addition, learning the interactions between electric and magnetic fields is very challenging for university students. Even after completing relevant studies, the students had difficulty in recognizing the symmetry relations between the electric and magnetic fields in all of the areas under study. Consequently, it appears that the concepts of electric and magnetic fields and their interrelations should be emphasized not only in the context of electromagnetism but also in other relevant areas such as electricity and optics. Explicit recommendations are presented in the discussion section at the end of this paper.