Density functional theory (DFT) is one of the successful theories in computational condensed matter.The theory is based on an idea that by knowing the ground state density of a system we can derive all properties of the system. According to this theory, the exchange-correlation energy of a system is a universal functional of the system density. The form of this universal functional is unknown, so we have to make approximation for exchange-correlation energy. Common approximations in DFT for exchange-correlation energy are LDA and GGA. These approximations have some faults which are detected very clearly in some examples. For example in LDA and GGA the site preference for CO on surface of Pt is predicted mistakenly. Or iron monoxide, FeO, which is an insulator with 2eV gap, is predicted as a metal. In this thesis we study these examples (CO/Pt(111) and FeO) deeply. In CO/Pt(111) we investigate the effect of different GGA functional on this problem and then we study the effect of a non-local functional and we show that by using a non-local functional we can improve the results. On the other hand we will show that there are some GGA functionals which can predict correct cite for adsorption of CO on Pt(111). To continue we study FeO under pressure and we show that even with method like as LDA+U we can not get correct behavior under pressure. For the solution of this problem we propose including spin-orbit interaction. Furthermore we study the possibility of orbital ordering in FeO by LDA+U.