The spin-1/2 Heisenberg antiferromagnets in one and two dimensions are important models in quantum magnetism in which many-body effects play a crucial role. Their collective excitations are associated with quasiparticles the interaction of which are difficult to describe. Neutron scattering offers a very powerful experimental technique to study these excitations. In addition, it can reveal the nature of exotic ground-states favored by competing frustrated interactions or by an applied magnetic field. This thesis presents neutron scattering studies of four materials, each representing a model magnetic system. • Cu(DCOO)2·4D2O (CFTD) is a model realization of the S =1/2 square-lattice antiferromagnet. It displays Néel order and its long-wavelength excitations are well described by renormalized spin-wave theory. In contrast, the excitations at the magnetic zone-boundary display anomalous dispersion and intensity close to (π, 0). A polarized neutron study of the anomaly additionally reveals the presence of a transverse continuum associated with a lineshape that extends to high energies. Results for the transverse and longitudinal continua are compared with Quantum Monte Carlo and fermionic Resonating Valence Bond theories. • (5CAP)2CuCl4 (CAPCC) is a S = 1/2 square-lattice antiferromagnet with modest saturation magnetic field Hs = 3.6 T and ∼ 20% antiferromagnetic interlayer coupling. Its spin excitations, measured above saturation are used to determine the microscopic exchange parameters of its Hamiltonian, while the presence of spontaneous magnon decay is investigated above the theoretically predicted threshold field H*= 0.76Hs. • CuSO4·5D2O is a model realization of the S = 1/2 antiferromagnetic Heisenberg chain. Its excitations are fully characterized in various regimes of applied magnetic field. In zero field, the presence of two- and four-spinon states is quantitatively confirmed, while the development of long-range Néel order is shown to preserve this picture qualitatively. In applied magnetic field, the excitations are studied with polarized neutrons and the existence of exotic psinons, anti-psinons and string-solutions continua is discussed. • LiCuVO4 is a S = 1/2 frustrated multiferroic chain material with competing ferromagnetic nearest and antiferromagnetic next-nearest neighbor interactions. Its magnetic structure is found to be a perfect circular cycloid the chirality of which can be tuned with an applied electric field. In crossed electric and magnetic fields, the behavior of the cycloid closely matches with that theoretically predicted from the spin supercurrent scenario. A magnetic-field induced transition to short-range longitudinal order is also evidenced with polarized neutrons. The present work was carried out in the Triple-Axis Spectrometers group at the Institut Laue Langevin in Grenoble, France and in the Laboratory for Quantum Mangetism at the EPFL, Switzerland.