Abstract: The latest progress in the study on LCPs is summarized. In particular, some new numerical algorithms for solving LCPs such as the modules-based matrix splitting methods are introduced. Some new results in the error analysis and perturbation analysis are summarized. At first, the linear complementarity problem is presented with its mathematical models and some notations. Secondly, the numerical algorithms for solving the linear complementarity problem are given. The iteration methods especially the module-based matrix splitting iteration methods proposed these years are summarized. Based on module equations, by introducing the idea of nonsmooth Newton.s method and preconditioned technique, two new methods, the modules-based nonsmooth Newton's method and the preconditioned modules-based matrix splitting iteration method, are established, which can converge faster than the existing module-based matrix splitting iteration methods. Then the error analysis of the solution of the linear complementarity problem is given with the new error bounds based on preconditioned technique, which is better than the error bounds given before. The results of the perturbation analysis of the solution of the linear complementarity problem are shown with the latest perturbation bounds.