Stability analysis of linear time-delay systems is always one of the hottest issues in control research fields. Especially after the establishment of the Wirtinger-based integral inequality, there is an upsurge in stability analysisof linear time-delay systems. The Lyapunov-Krasovskii(L-K) functional method is developing rapidly and has become the main way in studying the stability of time-delay systems. We mainly discuss recent advances of the inequality-based L-K functional method in stability analysis of linear time-delay systems. Firstly, we recall some typical integral and matrix inequalities and analyse their roles in reducing the conservatism of stability conditions. Secondly, we discuss some recently-developed L-K functionals. Finally, some conclusions are made and some problems are presented that need to be solved in the future for the stability of time-delay systems.