Thermodynamics and dielectric properties of nematic liquid crystals doped with various nanoparticles have been studied in the framework of a molecular mean-field theory. It is shown that spherically isotropic nanoparticles effectively dilute the liquid crystal material and cause a decrease of the nematic-isotropic transition temperature, while anisotropic nanoparticles are aligned by the nematic host and, in turn, may significantly improve the liquid crystal alignment. In the case of strong interaction between spherical nanoparticles and mesogenic molecules, the nanocomposite possesses a number of unexpected properties: The nematic-isotropic co-existence region appears to be very broad, and the system either undergoes a direct transition from the isotropic phase into the phase-separated state, or undergoes first a transition into the homogeneous nematic phase and then phase-separates at a lower temperature. The phase separation does not occur for sufficiently low nanoparticle concentrations, and, in certain cases, the separation takes place only within a finite region of the nanoparticle concentration. For nematics doped with strongly polar nanoparticles, the theory predicts the nanoparticle aggregation in linear chains that make a substantial contribution to the static dielectric anisotropy and optical birefringence of the nematic composite. The theory clarifies the microscopic origin of important phenomena observed in nematic composites including a shift of the isotropic-nematic phase transition and improvement of the nematic order; a considerable softening of the first order nematic-isotropic transition; a complex phase-separation behavior; and a significant increase of the dielectric anisotropy and the birefringence. *