We will review recent results obtained by longitudinal polarization analysis and spherical neutron polarimetry (SNP) on typical low-dimensional strongly correlated electronic systems (spin-Peierls CuGeo(3), high-T-c La0.85Sr0.15CuO4 and YBa2CU3O6+x, or spin-ladder Sr14Cu24O41), which all demonstrate the importance of polarized neutrons for studies of magnetic and structural inelastic contributions. In such systems, the hybridization between the structural and magnetic degrees of freedom is expected to give rise to non-negligible hybrid correlation functions, which can be detected and accurately investigated by neutron polarimetry. The interest of the SNP in inelastic scattering will be discussed through measurements on CuGeO3.