I thought that this question was very interesting because primates are the closest living relatives to humans. Primates are fascinating because they resemble a primitive or basal version of ourselves and at the same time are also quite different from us as well. There is a large number of primate species both in the African and Asian continents as well as in the Americas. Those species that are found in Africa and Asia are collectively called old world monkeys and apes. The species found in the Americas are known as new world monkeys. An interesting feature that many of the new world monkeys have that old world monkeys do not is a prehensile tail which can be used as a fifth limb. Another interesting difference is that thanks in part to their prehensile tails the new world monkeys are almost entirely arboreal while the old world monkeys are both terrestrial and arboreal.
A major distinction between old world monkeys and new world monkeys is the structure of the nose. In new world monkeys, or platyrrhines, the nostrils face sideways, while in old world monkeys, or catarrhines, they face downwards. The distinction between Old World monkeys or catarrhines, from apes depends on dentition because the number of teeth is the same in both, but they are shaped differently.
The old world monkeys are all in the family Cercopithecidae. The old world monkeys are partially omnivorous, but prefer plant matter which can form the bulk of their diet.
New World monkeys are comprised of five families: Callitrichidae, Cebidae, Aotidae, Pitheciidae, and Atelidae. The five families are within the Ceboidea superfamily. They eat fruits, nuts, insects, flowers, bird eggs, spiders, and small mammals.
Prosimians are a group of mammals which are defined as being primates, but are not monkeys or apes. They include, lemurs, bush babies, and tarsiers. They have characteristics that are more primitive or basal than those of monkeys and apes.