Stability is a fundamental issue for the practical applications of linear systems with time-varying delay. In order to reduce the conservatism of a stability criterion, lots of efforts have been made and a great number of results have been reported in the literature. In recent years, a class of novel integral inequalities have been proposed, which can provide tight bound for the integral terms appearing in the derivative of some Lyapunov-Krsovskii functional. This talk presents an overview of recent advances in stability analysis using the integral inequality approach, and some challenging issues as well.