Encapsulation of lanthanides ions inside a carbon cage gives a variety of structures with very different magnetic properties, including single molecule magnetism (SMM). When other non-metal ions (N, S, O) are encapsulated as well, short distance between metal ions and negatively-charged non-metal ions creates large single-ion magnetic anisotropy of encapsulated lanthanides. In such clusterfullerene SMMs, very large barriers of the relaxation of magnetization can be achieved.[1] Encapsulation of only two metal atoms gives a possibility to create unique 3-center spin systems featuring large localized magnetic moments of lanthanide ions and an unpaired semi-delocalized spin on the metal-metal bonding orbital. In such a system, giant exchange interactions emerge and couple magnetic moments of individual spins into a giant superspin structure with unusually high blocking temperatures of magnetization.[2] Importantly, slow relaxation of magnetization is preserved even when fullerene-SMMs are deposited onto metal substrates, which usually has a dramatic deteriorating effect on SMMs. This contribution will present an overview of the recent developments in the magnetism of EMFs in bulk samples as well as in submonolayers deposited on metallic substrates.