  Magnetically tunable Feshbach resonances were employed to associate cold
diatomic molecules in a series of experiments involving both atomic Bose as
well as two spin component Fermi gases. This review illustrates theoretical
concepts of both the particular nature of the highly excited Feshbach molecules
produced and the techniques for their association from unbound atom pairs.
Coupled channels theory provides the rigorous formulation of the microscopic
physics of Feshbach resonances in cold gases. Concepts of dressed versus bare
energy states, universal properties of Feshbach molecules, as well as the
classification in terms of entrance- and closed-channel dominated resonances
are introduced on the basis of practical two-channel approaches. Their
significance is illustrated for several experimental observations, such as
binding energies and lifetimes with respect to collisional relaxation.
Molecular association and dissociation are discussed in the context of
techniques involving linear magnetic field sweeps in cold Bose and Fermi gases
as well as pulse sequences leading to Ramsey-type interference fringes. Their
descriptions in terms of Landau-Zener, two-level mean field as well as beyond
mean field approaches are reviewed in detail, including the associated ranges
of validity.
