Kingdom Animalia
Phylum Chordata
Class Mammalia
Order Primates
Suborders Anthropoidea and Prosimii*
Primates have a comparatively large brain-case, and a trend away from instinct and towards reliance on social behavior to aid in survival. They also have stereoscopic vision, and because of this they have a post-orbital bar to keep the working of their jaw muscles from interfering with their eye movement. Most have opposable thumbs.
The Prosimians (Prosimii) are on the way out, living in Africa, Asia, India, and primarily in Madagascar. They have been slowly shrinking in number as the Anthropoids take over. About half the prosimians are nocturnal, and therefore lack color vision. They have prehensile tails and opposable thumbs, although their thumbs are not as opposable as the Anthropoidea. Prosimians include the Tarsier, Lemur, loris, and galago.
The Anthropoid (Anthropoidea) primates include the two infraorders, monkeys (Platyrrhini or New World Monkeys) and Apes (Catarrhini or Old World Monkeys/Old World Primates). Most of these are diurnal, and have color vision.
All the New World platyrrhine primates are monkeys. The Old World catarrhine primates are made up of monkeys and apes, some of which are Humans.
Platyrrhine monkeys have flat noses (hence the name), have 12 molars, are arboreal and herbivorous, and long limbs. They are all arboreal. They have 36 teeth (2.1.2.3./2.1.2.3.). They live in North, Central, and South America. The platyrrhines are divided into two families.
The Callithricidae: tamarins and marmosets. They are small, from the size of housecats to the size of mice. They do not have opposable thumbs or prehensile tails. They are sometimes said to be the most 'primitive' primates, because they seem to be the closest to our ancestors.
The Cebidae: Squirrel Monkey, Spider Monkey, Howler Monkey, Night Monkeys, Owl Monkeys, Titi Monkeys, Capuchins, Sakis, Uacaris, Woolly Monkeys, etc. They can get up to the size of a medium-sized dog. Many have strong prehensile tails, which are some of the strongest and most advanced in the primates.
Catarrhini primates that have narrow noses with the nostrils facing downwards, are diurnal, and do not have any prehensile tails. They have 32 teeth (2.1.3.3./2.1.3.3.). They are divided into two superfamilies.
Cercopithecoidea: Macaques, Baboons, Drills, Mandrills, Mangabeys, Guenons, Vervet Monkeys, Colobus Monkeys, Leaf Monkeys, Langurs, Snub-nosed Monkeys, Proboscis Monkeys, etc.
Live in Europe (now only in Gibraltar), Africa, and Asia. Most have tails, and all have fully opposable thumbs.
Hominoidea** (Apes):
Tailless primates, they have larger brains than the other primates and are adapted to an arboreal environment. Their shoulder joints are more flexible, their shoulder blade if further back, and they have a strong clavicle, all of which makes them good brachiators. (Humans too!)
* The suborders are sometimes divided differently--the tarsiiforms (Tarsiers) Behave like prosimians, but they don't have a rhinarium. The Anthropoidea/Prosimii divition puts the Tarsiers in with the prosimimians, because it focuses on behavior. People who wish to focus on physical traits (of which the rhinarium {wet nose} is the most obvious) will often split the order into Haplorhini (no rhinarium), and Strepsirhine (rhinarium {literally 'split nose'}).
** Hominoidea is not always broken up in this way. There are other ways of slicing up the Hominoidea, due to the fact that people weigh different traits differently.
You may often see it as:
Hylobatidae: Gibbons
Pongidae: Orangutans, Gorillas, and Bonobos, Chimpanzees.
Hominidae: Humans
This is apparently and older way of doing it, motivated by the desire to set humans apart from 'lower animals'.
References.
Biological Anthropology by Michael Alan Park
Linda Wolfe, Professor of Anthropology at East Carolina University
http://daphne.palomar.edu/primate/prim_4.htm
http://animaldiversity.ummz.umich.edu/chordata/mammalia/primates.html
http://www.u.arizona.edu/~vlandau/Study/Study1.htm Highly recommended.
Others.