This chapter addresses the stability analysis of linear dynamical systems represented by delay differential equations with a focus on the effects induced by the delay, seen as a parameter, on the dynamical behavior. More precisely, we propose a frequencysweeping framework for treating the problem, and the stability problem is reformulated in terms of properties of frequency-sweeping curves. The presentation is teaching-oriented and focuses more on discussing the main ideas of the method and their illustration through appropriate examples and less on explicit proofs of the results. Some applications from Life Sciences complete the presentation.