The purpose of this review is to provide a critical survey covering a few decades of growing interest in the application to polymer chemistry of the Diels–Alder (DA) reaction between furan and maleimide moieties. The major peculiarity of this specific combination of reagents is the fact that their click coupling to generate the DA adduct is thermally reversible, through the retro-DA reaction, at about 100°C, i.e., a viable and non-degradative temperature in terms of its application to practically all macromolecular structures. The use of furan derivatives constitutes an additional positive feature in this context, because of their renewable character. Attempts were made to insure a comprehensive coverage of the literature, which deals with vastly different approaches and aims concerning the chemistry, the polymer architectures and the possible application of the ensuing materials. The decision to cite all publications available on the subject was deliberate in the sense that in doing so, it was possible to examine them critically and highlight excellence and flaws.