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Magnetically tunable Feshbach resonances were employed to associate colddiatomic molecules in a series of experiments involving both atomic Bose aswell as two spin component Fermi gases. This review illustrates theoreticalconcepts of both the particular nature of the highly excited Feshbach moleculesproduced and the techniques for their association from unbound atom pairs.Coupled channels theory provides the rigorous formulation of the microscopicphysics of Feshbach resonances in cold gases. Concepts of dressed versus bareenergy states, universal properties of Feshbach molecules, as well as theclassification in terms of entrance- and closed-channel dominated resonancesare introduced on the basis of practical two-channel approaches. Theirsignificance is illustrated for several experimental observations, such asbinding energies and lifetimes with respect to collisional relaxation.Molecular association and dissociation are discussed in the context oftechniques involving linear magnetic field sweeps in cold Bose and Fermi gasesas well as pulse sequences leading to Ramsey-type interference fringes. Theirdescriptions in terms of Landau-Zener, two-level mean field as well as beyondmean field approaches are reviewed in detail, including the associated rangesof validity.Comment: 50 pages, 26 figures, to be published in Reviews of Modern Physics,  final version with updated reference

Production of cold molecules via magnetically tunable Feshbach resonances