I hardly feel that this group needs much introduction. The Anthropoidea (the name means 'man-like') are the monkeys, and everyone knows what a monkey is (Groucho Marx supposedly once claimed that the word 'duck' was the funniest in the English language, but I'm sure that the word 'monkey' mustn't be far behind). Modern-day anthropoids fall into two clades, the New World Platyrrhini (New World monkeys) and the Old World Catarrhini (Old World monkeys and apes, including humans). There is also a handful of fossil taxa that probably fall outside the crown group such as Parapithecidae and Eosimiidae. It seems pretty clear that the Anthropoidea were Old World in origin, possibly Asian (Beard & Wang, 2004). How the ancestors of the Platyrrhini managed to turn up in South America is something of a mystery - it seems most likely that they dispersed there from Africa, but how they managed to cross the Atlantic remains an open question (Schrago & Russo, 2003). However they did it, it is possible that the ancestors of the South American caviomorph rodent radiation arrived the same way at the same time (Schrago & Russo, 2003).
Anthropoids are fairly easy to recognise, or at least the modern ones are. The eyes are more vertically-positioned than in other primates, among other features. At some point, the ancestors of anthropoids also lost the ability to produce ascorbic acid (vitamin C), which is why we have to receive it from our diet (apparently the only other animals to suffer from this deficiency are guinea pigs). It has even been suggested that this loss has been a major factor in anthropoid evolution, as mutation increases in the absence of ascorbate's antioxidant effect (Challem, 1997). However, the rate of evolution of the hominoid (humans and apes) branch, at least, seems to have been reduced relative to other primates (Tëtushkin, 2003).
Beard, K. C. & J. Wang. 2004. The eosimiid primates (Anthropoidea) of the Heti Formation, Yuanqu Basin, Shanxi and Henan Provinces, People's Republic of China. Journal of Human Evolution 46 (4): 401-432.
Challem, J. 1997. Did the loss of endogenous ascorbate propel the evolution of Anthropoidea and Homo sapiens? Medical Hypotheses 48: 387-392.
Schrago, C. G., & C. A. M. Russo. 2003. Timing the origin of New World monkeys. Molecular Biology and Evolution 20 (10): 1620-1625.
Tëtushkin, E. Ya. 2003. Rates of molecular evolution of primates. Genetika 39 (7): 869-887 (transl. Russian Journal of Genetics 39 (7): 721-736.