Studies of quasimolecular states and transitions in atomic collisions are reviewed. The statistical theories of the quasimolecule based on the Thomas--Fermi model and the statistical approach to the process of ionization in collision of heavy atoms are discussed. A quantum theory of the quasimolecule is presented. Mechanism of ionization in a quasimolecule and the properties of quasimolecular autoionization states are discussed. Some exotic quasimolecules are described: superheavy, which are formed in the collision of heavy atoms (up to uranium); mesoquasimolecules, which arise in the collision of an atom and a mesonic atom; and quasimolecules formed by fission fragments. The fundamental properties of radiation from quasimolecules and the mechanisms of generating it are presented. In closing we indicate the prospects for applying quasimolecular effects in different fields of physics.