Short answers, pulled from the story.
New World monkeys are thought to have rafted across the Atlantic Ocean on floating mats of vegetation during the Eocene epoch, roughly 40 million years ago. At that time the Atlantic was narrower by perhaps a thousand kilometres, the Isthmus of Panama did not yet exist, and ocean currents favoured westward drift. Fossil evidence suggests there were at least two separate dispersal events from Africa to South America.
New World monkeys have flatter noses with sideways-facing nostrils, compared to the narrow downward-facing nostrils of Old World monkeys. They also have twelve premolars instead of eight, are the only primates with prehensile tails, and most lack the full trichromatic colour vision common in Old World species. Many form monogamous pair bonds with strong paternal care, a pattern uncommon in Old World primates.
The pygmy marmoset is the world's smallest monkey, measuring 14-16 cm in body length and weighing 120-190 g. At the other end of the New World monkey size range, the southern muriqui reaches 55-70 cm and weighs 12-15 kg.
Prehensile tails are found in New World monkeys but not uniformly across all species. Members of the family Atelidae, including spider monkeys, woolly monkeys, and howler monkeys, have fully prehensile tails capable of bearing their entire body weight. Capuchin monkeys have semi-prehensile tails useful for balance, and anatomical evidence shows the trait evolved at least twice independently through convergent evolution.
The classification by Rylands and Mittermeier in 2009 recognises five families: Callitrichidae, Cebidae, Aotidae, Pitheciidae, and Atelidae, all grouped in the superfamily Ceboidea. Earlier classifications used as few as two families or as many as four, and the arrangement of subfamilies within those families has also shifted across different authorities.
Most New World monkeys have limited colour vision compared to Old World monkeys. Males and homozygous females are dichromatic, relying on a single gene on the X-chromosome for medium and long wavelength perception. Only heterozygous females can achieve trichromatic vision. Howler monkeys of genus Alouatta are the exception, being the only New World monkeys with full trichromacy across the whole population.