The article deals with the difficulties encountered in the study of the topic “Skew lines” — one of the most difficult in the school course of geometry. It identifies the challenges of historical and methodological nature. A brief historical review related to the presence of the concepts of «distance» and «angle» between skew lines in the educational literature is given. The ways of overcoming the highlighted difficulties, both in the study of solid geometry and in the study of geometry by future teachers of mathematics is given.