We will review recent results obtained by longitudinal polarization analysis (LPA) and spherical neutron polarimetry (SNP) on typical "low-dimensional" strongly correlated electronic systems (spin-Peierls CuGeO3, High-T-c YBa2Cu3O6+x...), which all demonstrate the importance of polarized neutrons for studies of the 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 investigated accurately by neutron polarimetry. The interest of the SNP in inelastic scattering will be discussed through measurements on CuGeO3.