In this thesis, we will review the infinite derivative theories of gravitational interaction. Infinite derivative extension of gravity is based on the addition of nonlocal terms in the Einstein-Hilbert action. The thesis starts with a short introduction regarding the problems which one must solve to obtain a valid description of the gravitational interaction. After that, we will show how one can obtain the infinite derivative gravity action which is quadratic in curvature terms. Using corresponding equations of motion in the weak-field approximation we will show that the infinite derivative gravity removes singular behaviour of the gravitational potential whose source is the point mass. Also, the gravitational potential is devoid of an event horizon. Furthermore, we will see how the modification of Einstein’s field equations due to the presence of nonlocal terms affects the cosmological solution. We will focus on the bouncing solution which gives rise to a geodesically complete the de Sitter Universe. The final part of this thesis deals with the classical perturbations of the cosmological solution which must produce the same results as in General Relativity when nonlocal terms are suppressed.