<p>Inequality techniques have become essential tools for the stability analysis of time-varying delay systems. This paper presents a comprehensive survey of recent research trends in three key inequality techniques: integral inequalities, reciprocally convex combination inequalities, and matrix-valued polynomial inequalities. First, we examine the theoretical foundations and comparative advantages of various integral inequalities, highlighting their contributions to reducing conservatism in stability conditions. Second, we analyze the development of reciprocal convex combination inequalities derived from indirect integral inequalities. Finally, we provide an in-depth review of matrix-valued polynomial inequalities, which have emerged as a central focus of current research. In conclusion, we discuss the current challenges along with potential future directions for advancing inequality-based stability analysis.</p>