This paper overviews the literature pertaining to the stability analysis of systems with delay-dependent coefficients, which can arise from various scientific and engineering applications. Research on Stability analysis for systems with a single delay is first reviewed, followed by a discussion of some techniques also applicable to the multiple-delay case. We attempt to provide the main ideas of various stability analysis methods, the insight gained from them as well as their specific advantages and limitations. Potential directions for future research are suggested.