  Recent developments concerning localized-magnon eigenstates in strongly
frustrated spin lattices and their effect on the low-temperature physics of
these systems in high magnetic fields are reviewed. After illustrating the
construction and the properties of localized-magnon states we describe the
plateau and the jump in the magnetization process caused by these states.
Considering appropriate lattice deformations fitting to the localized magnons
we discuss a spin-Peierls instability in high magnetic fields related to these
states. Last but not least we consider the degeneracy of the localized-magnon
eigenstates and the related thermodynamics in high magnetic fields. In
particular, we discuss the low-temperature maximum in the isothermal entropy
versus field curve and the resulting enhanced magnetocaloric effect, which
allows efficient magnetic cooling from quite large temperatures down to very
low ones.
