Strongly frustrated antiferromagnets such as the magnetic molecule {Mo₇₂Fe₃₀}, the kagome, or the pyrochlore lattice exhibit a variety of fascinating properties like low-lying singlets, magnetization plateaus as well as magnetization jumps. During recent years exact many-body eigenstates could be constructed for several of these spin systems. These states become ground states in high magnetic fields, and they also lead to exotic behavior. A key concept to an understanding of these properties is provided by independent localized magnons. The energy eigenvalue of these n-magnon states scales linearly with the number n of independent magnons and thus with the total magnetic quantum number M = Ns − n. In an applied field this results in a giant magnetization jump which constitutes a new macroscopic quantum effect. It will be demonstrated that this behavior is accompanied by a massive degeneracy, an extensive (T = 0)-entropy, and thus a large magnetocaloric effect at the saturation field. The connection to flat band ferromagnetism will be outlined.