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Rydberg states are electronically excited states, the spectral position of which can be described by Rydberg’s well-known formula . Rydberg states of atoms and molecules possess very unusual physical properties which all scale as integer multiples of the principal quantum number n , their polarizability as n7, the van der Waals interaction between two Rydberg atoms or molecules as n11, the maximal electric dipole that can be induced by an electric field as n4, the threshold field for field ionization as n-4, the spacing between adjacent states of a given Rydberg series as n-3, the absorption cross section from the ground state as n-3, the transition moment between neighboring Rydberg states as n2, their lifetime as n3, etc. These physical properties and their rapid variation with n form the basis of a growing number of applications of Rydberg states in chemistry and physics.
The talk will begin with an overview of the properties of Rydberg states and their applications in physics and chemistry. Then, the close relationship between Rydberg states, electron-ion collisions and photoionization  will be explained and illustrated by recent high-resolution spectroscopic investigations, using ultra-narrow VUV laser sources and millimeter-wave radiation sources, in which the role of nuclear spins in high Rydberg states, in electron-ion collisions and in photoionization could be studied in detail for the first time, both in atomic  and molecular  systems.
The last part of the talk will be devoted to a description of new experiments in which we have used the large dipole moments (more than 1000 Debye) that can be induced by electric fields in high Rydberg states to control their translational motion and to generate samples of translationally cold (T < 1K) atoms and molecules [6,7].
 J. R. Rydberg, Z. Phys. Chem. 5, 227 (1890)
 T. F. Gallagher, Rydberg Atoms (Cambridge University Press, Cambridge 1994)
 Ch. Jungen (Ed.), Molecular Applications of Quantum Defect Theory (IOP Publishing, Bristol, 1996)
 Th. A. Paul and F. Merkt, Phys. Rev. A 79, 022505 (2009)
 H. J. Wörner, S. Mollet, Ch. Jungen and F. Merkt, Phys. Rev. A 75, 062511 (2007)
 S. D. Hogan and F. Merkt, Phys. Rev. Lett. 100, 043001 (2008)
 S. D. Hogan Ch. Seiler and F. Merkt, Phys. Rev. Lett. 103, 123001 (2009)