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Recent developments concerning localized-magnon eigenstates in stronglyfrustrated spin lattices and their effect on the low-temperature physics ofthese systems in high magnetic fields are reviewed. After illustrating theconstruction and the properties of localized-magnon states we describe theplateau and the jump in the magnetization process caused by these states.Considering appropriate lattice deformations fitting to the localized magnonswe discuss a spin-Peierls instability in high magnetic fields related to thesestates. Last but not least we consider the degeneracy of the localized-magnoneigenstates and the related thermodynamics in high magnetic fields. Inparticular, we discuss the low-temperature maximum in the isothermal entropyversus field curve and the resulting enhanced magnetocaloric effect, whichallows efficient magnetic cooling from quite large temperatures down to verylow ones.Comment: 21 pages, 10 figures, invited paper for a special issue of "Low  Temperature Physics " dedicated to the 70-th anniversary of creation of  concept "antiferromagnetism" in physics of magnetis

Localized-magnon states in strongly frustrated quantum spin lattices