Until not very long ago, it was widely accepted that lens-based (far-field) optical microscopes cannot visualize details much finer than about half the wavelength of light. The advent of viable physical concepts for overcoming the limiting role of diffraction in the early 1990s set off a quest that has led to readily applicable and widely accessible fluorescence microscopes with nanoscale spatial resolution. Here I discuss the principles of these methods together with their differences in implementation and operation. Finally, I outline potential developments.