Abstract This talk will cover two recent papers of the speaker. 1. We give new error bounds for the linear complementarity problem(LCP) where the involved matrix is a P-matrix. Computation of rigorous error bounds can be turned into a P-matrix linear interval system. The new error bound is sharper than the Mathias-Pang error bound. Moreover, for the involved matrix being an H-matrix with positive diagonals, an error bound can be found by solving a linear system of equations. Preliminary numerical results show that the proposed error bound is efficient for verifying accuracy of approximate solutions. 2. We define a new fundamental constant associated with a P-matrix and show that this constant is sharper than the Mathias-Pang constant in deriving perturbation bounds for the P-matrix LCP. Moreover, this constant defines a measure of sensitivity of the solution of the P-matrix LCP.