Although electromagnetism is an important component of upper secondary school physics syllabuses in many countries, there has been relatively little research on students' understanding of the topic. A written test consisting of 16 diagnostic questions was developed and used to survey the understanding of electromagnetism of upper secondary school students in Turkey (n = 120) and England (n = 152). A separate test consisting of 10 questions on the visualization of spatial rotation was used to investigate the hypothesis that students' ability to visualize three-dimensional situations from two-dimensional representations might influence learning of electromagnetism. Many students responses showed misunderstandings and inconsistencies that suggested they did not have a coherent framework of ideas about electromagnetism. Common errors included confusing electric and magnetic field effects, seeing field lines as indicating a "flow", using cause-effect reasoning in situations where it does not apply, and dealing with effects associated with the rate of change of a variable. Performance on the spatial rotation test was, however, only weakly correlated with performance on the electromagnetism questions. The findings suggest the need to develop teaching strategies that help students to visualize magnetic field patterns and effects, and assist them in integrating ideas into a more coherent framework. (Contains 7 tables and 1 figure.)