In the talk I will report on a series of our work in magnetic exchange interaction：We introduce an efficient method of computing magnetic exchange interactions in systems with strong correlations. It is based on a magnetic force theorem that evaluates linear response due to rotations of magnetic moments and uses a generalized spectral density functional framework allowing us to explore several approximations ranging from local density functional to exact diagonalization based dynamical mean field theory. This technique has been successfully used for a variety of materials. Considering the spin orbit coupling (SOC) as perturbation, we extract the general expression of a bilinear spin Hamiltonian, including isotropic exchange interaction, antisymmetric Dzyaloshinskii-Moriya (DM) interaction and symmetric Г term. Though it is commonly believed that the magnitude of the DM and Г interaction correspond to the first and second order of SOC strength λ respectively, we clarify that the term proportional to λ2 also has contribution to DM interaction. I will present the numerical method to calculate it. I will also introduce our several other works in this field.