The question is different for apes and for monkeys. Humans are definitely not descending from monkeys, instead both humans and monkeys have a common ancestor, and both are higher primates (think about it more like siblings than parent-child relationship).
As far as apes are concerned: humans are apes. We are apes together with other apes, such as bonobos and chimpanzees. We have a common ancestor, who was an ape too, so you could say that we are descended from apes (but not today's apes).
