Very widespread notion, but disregarded as specific object of study, the “limit case” reveals itself as a dart thrown from the human mind to probe the resistance of a given domain. If the most evident feature of the limit (or borderline or edge) cases is the amplification, or the reset, of some salient features to the point of being off line with respect to the genus to which they belong, they always subvert the standard conditions by denouncing a mismatch. In the first place, it is a mismatch between the discontinuity im­posed by the concepts and a continuity that one might observe in reality, which gives rise to problems of transition, border and categorization. The limit cases – exceptional and sometimes catastrophic puzzles – each time take on different looks: degenerate cases, breaking points, exceptional cases, zero degrees, extreme fictions, paradoxes, ideal models, all the way to cases of coincidentia oppositorum or issues of sheer vagueness.