The history of Rydberg states in atoms and molecules will be briefly summarized. If the ground state of a molecular system is unstable (as for example two He atoms) while most excited states are stable Rydberg states, we may describe the system as a Rydberg molecule. The simplest diatomic example is the
He2 molecule, while the simplest polyatomic system would be the
H3 molecule discovered only in 1979. In recent years many other examples have been studied and will be briefly summarized.