Organogels are an important class of gels, and are comparable to hydrogels owing to their properties as liquid-infused soft materials. Despite the extensive choice of liquid media and compatible networks that can provide a broader range of properties, relatively few studies are reported in this area. This review presents the applicability of organogels concerning their choice of components, unique properties, and applications. Their distinctive features compared to other gels are discussed, including multi-stimuli responses, affinity to a broad range of substances, thermal and environmental stability, electronic and ionic conductivity, and actuation. The active role of solvents is highlighted in the versatility of organogel properties. To differentiate between organogels and other gels, these are classified as gels filled with different organic liquids, including highly polar organic solvents and binary solvent systems. Most promising applications of organogels as sophisticated multifunctional materials are discussed in light of their unique features.