The molecular chemistry of the f-elements, i.e. the lanthanides and actinides, is traditionally dominated by the use of carbon, nitrogen, oxygen or halide ligands. However, the use of metal-based fragments as ligands is underdeveloped, which contrasts to the field of d-block metal-metal complexes that have developed extensively over the last 50 years. Consequently, the use of metal-based fragments as ligands to the f-elements may be regarded as 'non-traditional'. This review outlines the development of compounds that possess f-element-metal bonds that may be described as polarized covalent or donor-acceptor in nature. For this review, the f-element is defined as (i) a group 3 or lanthanide metal: scandium, yttrium and lanthanum to lutetium or (ii) an actinide metal: thorium or uranium, and the metal is defined as a d-block transition metal, or a p-block triel (group 13, aluminium or gallium), a tetrel (group 14, silicon, germanium or tin), or a pnictide (group 15, antimony or bismuth) metal. Silicon, germanium and antimony are traditionally classified as metalloids, but we include them in this review for completeness. This review focuses on complexes that have been unambiguously structurally authenticated by single crystal X-ray diffraction studies, and novel aspects of their syntheses, properties and reactivities are highlighted.