Abstract The review is devoted to compounds and materials demonstrating extremely high magnetic hardness. The recent advances in the synthesis of modern materials for permanent magnets are considered, and a range of exotic compounds interesting for fundamental research is described. The key details of chemical composition, crystal structure and magnetic microstructure responsible for the appearance of high magnetic anisotropy and giant coercivity are analyzed. The challenges of developing the title materials are noted and strategies for their solution are discussed. The bibliography includes 389 references.