 Paradoxes of this kind have been known since antiquity (the standard Liar is attributed to the Greek philosopher Eubulides, probably the greatest paradox-producer of antiquity). But they were thrown into prominence by developments in the foundations of mathematics around the turn of the twentieth century. In the case of each paradox, there appears to be a perfectly sound argument ending in a contradiction. If the arguments are sound, then dialetheism is true. Of course, many have argued that the soundness of such arguments is merely an appearance, and that subtle fallacies may be diagnosed in them. Such suggestions were made in ancient and medieval logic; but many more have been made in modern logic—indeed, attacking the paradoxes has been something of a leitmotiv of modern logic. And one thing that appears to have come out of this is how resilient the paradoxes are: attempts to solve them often simply succeed in relocating the paradoxes elsewhere, as so called ‘strengthened’ forms of the arguments show. Let us have a look.