General relativity is a align=left There are different motivations for modifying and completing this theory. In this thesis we investigate the higher derivatives theories of gravity. Lovelock models are those with similar characteristics with general relativity. For example the equivalence of the Palatini and metric formulations, is a propery of Einestein gravity theory. This is also the case for the Lovelock theories. As a special case we investigate the Einestein-Gauss-Bonnet gravity in details. We linearize this model around the AdS solution and find that propagator of this model is massless graviton. We find that this theory contains ghost-like solution. There is a critical point in which kinetic term vanishes and Einestein-Gauss-Bonnet gravity describes a gravity theory without graviton. We add curvature squared terms to Einestein-Hilbert action and linearize this model, as well. We consider this theories of gravity in four dimensions and D dimensions. This theories of gravity describe a massless spin-2 graviton, a massive spin-2 part and a massive scalar. This theories of gravity also suffer from having ghosts. There is a critical point in which massive scalar is absent, massive spin-2 field becomes massless and the energies of excitations of the remaining massless graviton vanish. The lacking of kinetic term is unusual from the point of view of field theories and its physical implication is not clear. We study AdS wave solutions in these models and find that at the critical points these models admit logarithmic solutions. Within the framework of the AdS/CFT duality, these models may provide gravity descriptions for logarithmic conformal field theories in the boundary.