Abstract: Infinitesimals, have been considered, especially in calculus, since ancient times. Generally regarded as vague fancies, despite their marvelous success, their use was finally justified... and dispensed with by the introduction of the modern notion of limit in the golden age of austere mathematics, mainly in the work of Cauchy and Weierstrass. However, to appropriate the words of a near contemporary, reports of their death were greatly exaggerated. Within a generation of their evaporation, infinitesimals had been revived, and it being the 19th century, they were now vim and rigorous. While appearing in at least one popular calculus test, by the mid 20th century, (that most inflexible, uncompromising, ironhanded, brutal age of Turing machines, set forcing and categorical abstract nonsense), and they were more often found moonlighting in the service of non-Archimidean geometry in abstract algebra texts. Then after nigh on a century haunting the wilderness, certain infinitesimals returned to the limelight in Robinson's theory of non-standard analysis. Called hypperreals, they were well-founded but..urrhrrm.. nonconstructive, thus maintaining their pedigreed air of mystery. There is now a small zoo of infinitesimals and as luck would have it, many of them are constructive, which ought to be enough to satisfy even the most strict finitist. Nonetheless, the cagey infinitesimals remain more or less controversial and to this day some very curmudgeonly mathematicians, the ultrafinitists, wish their departure and release. We shall take a brief tour among the ever contentious critters and their infinite cousins. No calculus is required.