Searches for new materials for electro-optic devices has led to the creation of heterogeneous materials in which liquid crystals (LCs) are dispersed in rigid matrices (confined/dispersed LCs) or filled with Aerosil particles forming flexible network (Filled LCs). We present the results of investigations of the influence of the confinement, interface and heterogeneity on relaxations of collective and molecular origin on LCs by photon correlation spectroscopy (PCS) and broadband dielectric spectroscopy (DS). The experiments show significant changes in the physical properties of LC confined in random porous medium and filled with Aerosil particles. The spatial confinement and a highly developed solid material-LC interface in these materials have a strong influence on physical properties of LC that is resulted in: appearance of at least two new dielectrically active modes, absent in the bulk LC and existence of slow glass-like relaxation process detected in both PCS and DS experiments. The collective relaxation processes due to fluctuations of director reorientations in these materials shows glass-like behavior. It is of non-Debye type and the temperature dependencies of the relaxation times obey Vogel-Fulcher law. Confinement modifies even bulk-like relaxation process due to the rotation of molecules around short axes, investigated in BDS experiment.