Photochemical stability is one of the most important parameters that determine the usefulness of organic dyes in different applications. This Review addresses key factors that determine the dye photostability. It is shown that photodegradation can follow different oxygen-dependent and oxygen-independent mechanisms and may involve both 1S1-3T1 and higher-energy 1Sn-3Tn excited states. Their involvement and contribution depends on dye structure, medium conditions, irradiation power. Fluorescein, rhodamine, BODIPY and cyanine dyes, as well as conjugated polymers are discussed as selected examples illustrating photobleaching mechanisms. The strategies for modulating and improving the photostability are overviewed. They include the improvement of fluorophore design, particularly by attaching protective and anti-fading groups, creating proper medium conditions in liquid, solid and nanoscale environments. The special conditions for biological labeling, sensing and imaging are outlined.