Fluorescent proteins have revolutionized life sciences because they allow noninvasive and highly specific labeling of biological samples. The subset of "phototransformable" fluorescent proteins recently attracted a widespread interest, as their fluorescence state can be modified upon excitation at defined wavelengths. The fluorescence emission of Reversibly Switchable Fluorescent Proteins (RSFPs), in particular, can be repeatedly switched on and off. RSFPs enable many new exciting modalities in fluorescence microscopy and biotechnology, including protein tracking, photochromic Förster Resonance Energy Transfer, super-resolution microscopy, optogenetics, and ultra-high-density optical data storage. Photoswitching in RSFPs typically results from chromophore cis-trans isomerization accompanied by a protonation change, but other switching schemes based on, e.g., chromophore hydration/dehydration have also been discovered. In this chapter, we review the main structural features at the basis of photoswitching in RSFPs.