The complete stability of time-delay systems is a fundamental academic problem in the control field, which has attracted wide attention for a long time. However, people may tend to have some incorrect understanding of the complete stability. In the open literature, no dedicated survey paper has been reported so far concerning this topic. In this survey paper, the complete stability of time-delay systems is reviewed in terms of preliminaries, existing results, technical difficulties, and the idea of solution. Finally, a recently-established tool, the new frequency-sweeping framework, is introduced. Within this framework, the complete stability is systematically solved for the first time.