Abstract: Fast forward and inverse algorithms for complex targets in controlled source electromagnetic exploration (CSEM) is a intense topic in current years. In this paper, the overview of the effective solvers used in complex targets imaging via CSEM is presented. With the analysis of application of modeling and imaging for complex targets via differential methods, it is indicated that the effective parallel computing and the needed boundary conditions are crucial important for the really application of differential methods. The 2D and 2.5D fast imaging algorithms for exploration with terrain based on integral equation (IE) modeling is few considered over the past few years, which is concluded in this paper. The fast algorithms presented in this work will be effectively applied in large scale exploration with high accuracy and resolution via CSEM. The effectiveness of the fast solvers is validated by 2D and 2.5D case studies using integral equation modeling.