General introduction to modified gravity is given. Overview of different models is presented. Special attention is paid to F(R) gravity and modified Gauss-Bonnet gravity. It is discussed realistic exponential model of F(R) gravity which unifies the early-time inflation with dark energy epoch.

The observational bounds for such model are given and comparison with LCDM is done. Modified Gauss-Bonnet gravity is discussed in relation with recent GW event. Some astrophysical applications to neutron stars are also described