In modern biotechnological science, there is a need for visualization of objects under study at the levels of cells, organelles, and individual molecules. Prominent among imaging methods are the methods based on the detection of fluorescence from the fluorophores with which objects under study are labeled. Fluorescent proteins (FPs) are very popular as genetically encoded fluorescent labels for lifetime imaging of target structures and processes in living systems. One of the key characteristics of FPs is their photostability, i.e., their resistance to photochemical reactions that quench the fluorescence signal. This review describes the currently known molecular mechanisms underlying photobleaching and the methods used to improve the photostability of fluorescent proteins.