That's an excellent question. Man did not evolve from monkeys and apes. Man, monkeys, and apes ALL evolved from a common ape-like ancestor over 20 million years ago, at which time monkeys split off from the evolutionary line. Monkeys are strictly New World primates, found only in Central and South America. Apes are strictly Old World primates, found only in Africa and Asia. Humans and apes had common ancestry until about 5-8 million years ago, which explains why we share so much more of our DNA with apes, particularly chimpanzees, than we do with monkeys. At that time, human ancestors split off from the apes. So for the last 5-8 million years, humans, monkeys, and apes have evolved along separate evolutionary lines, which explains why monkeys and apes still exist. In that sense, monkeys and apes are as evolved as humans, but they are adapted to the environments in which they live. A good site where you can learn more about human evolution is the Smithsonian Institution Human Origins Program webpage.
http://anthropology.si.edu/humanorigins/
A Thought From Yivo 13
I think that when we evolved from primates the primates had evolved from somthing else, and when we evolve again primates will become the next humans.