The spatial distribution of neutrons and protons in a stable nucleus is nearly equal. This can change drastically in particular for very neutron-rich nuclei. In the light mass region so-called ‘halo nuclei’ have been found. They consist of a compact core nucleus ‘surrounded’ by 1 one or more very loosely bound neutrons. The ‘size’ of these nuclei can be as large as that of a heavy stable nucleus (like Pb-208) and is determined by the binding energy of the nucleus. Mass measurements on very neutron-rich isotopes help to understand the properties of this exotic systems and to predict where other halo nuclei exist.