This article reviews the main physical properties of atomically thin semiconductors and the electronic devices based on them. We start with graphene, describing its physical properties and growth methods, followed by a discussion of its electronic device applications. Then, transition metal dichalcogenides (TMDs) are analyzed as a prototype of atomically thin semiconductors, their physical properties, growth methods, and electronic devices are discussed in detail. Finally, non-layered semiconducting membranes with thicknesses ranging from a few nanometers to about 50 nm, and considered as counterparts of atomically thin semiconductors, are analyzed, and their applications presented.