The theoretical results obtained in Uzbekistan in the field of relativistic astrophysics and cosmology are presented. In particular electrostatic plasma modes along the open field lines of a rotating neutron star and Goldreich-Julian charge density in general relativity are analyzed for the rotating and oscillating magnetized neutron stars. The impact that stellar oscillations of different type (radial, toroidal and spheroidal ones) have on electric and magnetic fields external to a relativistic magnetized star has been investigated. A study of the dynamical evolution and the number of stellar encounters in globular clusters with a central black hole is presented. Perturbation features and instabilities of the large-scale oscillations on the background of the non-linearly pulsating isotropic and isotropic Ω-models are studied. The non-stationary dispersion equation of the sectorial perturbations for the general case and the results of certain oscillation mode analysis are given. The model composed as the linear superposition of two other models was constructed and the stability of this model is studied. In a cosmological setting the theory of macroscopic gravity as a large-distance scale generalization of general relativity has been developed. Exact cosmological solutions to the equations of macroscopic gravity for a flat spatially homogeneous, isotropic space-time are found. The gravitational correlation terms in the averaged Einstein equations have the form of spatial curvature, dark matter and dark energy (cosmological constant) with particular equations of state for each correlation regime. Interpretation of these cosmological models to explain the observed large-scale structure of the accelerating Universe with a significant amount of the nonluminous (dark) matter is discussed.