Further miniaturisation of magnetic storage devices requires an advent of new types of magnets, since classical ferromagnetic materials show lack of remanence at nano- and subnanoscale. A single atom can represent the smallest possible bit of information. Even though the isolated single atoms are paramagnetic, the interaction of surface adsorbed atoms with a substrate can result in high magnetic anisotropy energy and long magnetisation lifetime. In this thesis the magnetic properties of surface supported rare-earth single atoms are investigated with X-ray absorption spectroscopy, X-ray magnetic circular dichroism and multiplet simulations. The first goal of the project was to find new adatom/substrate combinations that exhibit a long adatom magnetic lifetime, possibly extending the current limits of the atomic magnetic moment stability to higher temperatures and longer spin relaxation times. The second objective was to implement the external electric field control of the adatom magnetic properties. Firstly, we present the experimental and theoretical research on Dy and Ho single atoms deposited on BaO. A comparison of our results with similar studies sheds light on the impact of the substrate crystal field, in particular Dy-O bond covalency, on the magnetic stability of the rare-earth adatoms. Next, the detailed experimental investigation of Dy single atoms on ZnO is presented. This adatom/substrate pair is used as first attempt to implement the electric field control of the adatom magnetic properties. Lastly, we study the Dy adatoms on graphene layers grown on various metals. The vibrational modes of the metallic substrates are shown to strongly affect the Dy spin lifetime, while addition of a second graphene layer does not allow to significantly improve the adatom magnetic stability.