Monkeys are part of the Order of Primates, a group of mammals that include prosimians (like lemurs), and anthropoids (like monkeys, apes and humans). Primate-like mammals (proto-primates) probably begin to emerge in the Paleocene Epoch in the Tertiary Period (after 65 million years ago. This is the beginning of the Cenozoic Era(Age of Mammals and Birds), but there may have been some primate-like animals in the Late Cretaceous (prior to 65 million years ago, the Cretaceous is the last period of Mesozoic, the age of Dinosaurs it is when you get the Raptors and the T-Rex).
The first proto-primatesmwere small and probably closely resembled the modern tree shrew. True primates (Prosimians) seem to have emerged in the Eocene Epoch circa 55 million years ago. Modern Prosimians include Lemurs, Tarsiers and Lorises. Most of the living prosimians can be found on Madagascar and they are nocturnal (active at night) unlike Monkeys which tend to be diurnal (active during the day).
The ancestors of modern Monkeys split off from Prosimians forming the suborder anthropoidea. This occurred in the Late Eeocene or Early Oligocene (circa 40 million years ago) but the record is sketchy. These are not the monkeys we see today but ancesteral forms. New World Monkeys (Platyrrhine) split off from Old World Monkeys (Catarrhine) , around 30 million years ago. All of the Monkeys from this period are extinct.
Monkeys are thus a branch of the same suborder of Primates as humans and apes. Apes split off from Monkeys during the Miocene some 21 million years ago. The hominids (ancestors of humans) split off from apes between 5-8 million years ago during the late Miocene/Early Pliocene)
Prosimians and Monkeys declined during the Miocene and there was an explosion of apes. Monkeys later made a recovery and became ultimately more successful than apes, radiating into many forms.
Monkeys did not stay still, but continued to evolve down to the modern age. So the modern monkeys should be regarded as PRIMATE COUSINS to apes and humans and not ANCESTORS.