Photoinduced reactions play an important role in the photocycle of fluorescent proteins from the green fluorescent protein (GFP) family. Among such processes are photoisomerization, photooxidation/photoreduction, breaking and making of covalent bonds, and excited-state proton transfer (ESPT). Many of these transformations are initiated by electron transfer (ET). The quantum yields of these processes vary significantly, from nearly 1 for ESPT to 10-4-10-6 for ET. Importantly, even when quantum yields are relatively small, at the conditions of repeated illumination the overall effect is significant. Depending on the task at hand, fluorescent protein photochemistry is regarded either as an asset facilitating new applications or as a nuisance leading to the loss of optical output. The phenomena arising due to phototransformations include (i) large Stokes shifts, (ii) photoconversions, photoactivation, and photoswitching, (iii) phototoxicity, (iv) blinking, (v) permanent bleaching, and (vi) formation of long-lived intermediates. The focus of this review is on the most recent experimental and theoretical work on photoinduced transformations in fluorescent proteins. We also provide an overview of the photophysics of fluorescent proteins, highlighting the interplay between photochemistry and other channels (fluorescence, radiationless relaxation, and intersystem crossing). The similarities and differences with photochemical processes in other biological systems and in dyes are also discussed.