Abstract
This paper presents and discusses some facts from the history of research on the theory of absolute stability, which was brought to life by the well-known Lur'e Problem. Special attention is paid to hypotheses and examples that accompanied the progress in this field and exerted a significant influence on it. Various methods, which are in use in the theory of absolute stability, are considered. The list of references comprises papers, reviews and monographs, which form a rather complete notion of the history and progress of the theory of absolute stability.
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