New phenomena characteristic of one-dimensional magnetism have been studied in model systems: quantum effects in one-dimensional Heisenberg ferromagnets (1D-HF) withS = 1/2 and in one-dimensional Heisenberg antiferromagnets (1D-HAF) withS = 1; peculiar anisotropic behaviour of electron spin resonance (ESR) at low frequency and high temperature. The magnetic susceptibility in (CH3)4NCuCl3 and (C6H11NH3)CuBr3, close to theS = 1/2, sD-HF show the expected deviation from the classical behaviour while the recently predicted quantum energy gap for the 1D-HAF is observed in Ni(C2H8N2)2NO2ClO4. Low frequency ESR in (CH3)4NMnCl3, the archetype of 1D classical AF, is highly sensitive to the polarization of the oscillating field. In particular, for field direction along the chain axis, the signal is strongly enhanced while it remains at its expected value for perpendicular orientation. This behaviour is related to the axial symmetry of the system.