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Quite a few low-dimensional magnets are quantum-disordered ``spin liquids''with a characteristic gap in the magnetic excitation spectrum. Among these areantiferromagnetic chains of integer quantum spins. Their generic feature arelong-lived massive (gapped) excitations (magnons) that are subject to Zeemansplitting in external magnetic fields. The gap in one of the magnon branchesdecreases with field, driving a soft-mode quantum phase transition. The systemthen enters a qualitatively new high-field phase. The actual properties at highfields, particularly the spin dynamics, critically depend on the system underconsideration. Recent neutron scattering studies of organometallic polymercrystals NDMAP (Haldane spin chains with anisotropy) and NTENP (dimerized S=1chains) revealed rich and unique physics.Comment: 8 pages, 9 figures, semi-plenary lecture at the LT24 conference,  Orlando, Florida, August 200

Neutron Scattering Study of Quantum Phase Transitions in Integer Spin Chains