A wide range of problems in the natural sciences, economics, and engineering are modeled as linear complementarity problems. Interior point methods have been used for developing efficient solvers for such problems. However, until recently there has been a gap between theory and practice in the sense that the best theoretical computational complexity results were obtained for interior point methods acting in a small neighborhood of the central path, while the best practical performance was achieved by interior point methods acting in wide neighborhoods of the central path. The talk presents a survey of some new results that have closed this gap and have proposed new interior point methods that seem very promising in practical applications.