The resolution of a microscope using lenses and visible light has been limited by diffraction to ~ 200 nm. We show that this barrier can be broken through reversible saturable optical (fluorescence) transitions (RESOLFT). First put forward as Stimulated Emission Depletion (STED) and Ground State Depletion GSD) microscopy, RESOLFT concepts overcome diffraction by a saturated transition between two marker states, effected with a light featuring an intensity zero. Abbe's equation is extended to [Delta]x ~= [lambda] / (2 ? n ? sin a?* sqr (1 + I / Isat)). Isat is the intensity required for saturating the transition and I is the one applied. [Delta]x can be continuously decreased by increasing I/Isat. We report on STED- microscopy with fluorescence spot sizes down to 16 nm, i.e. ~ [lambda]/50. STED also allows fluorescence correlation spectroscopy with subdiffraction probing volumes. Populating the marker's triplet state as well as the 'switching' between conformational states in GFP-like proteins entail ultralow Isat, which should enable nanoscale resolution even with a lamp.