This is an old one that really grates on the evolutionist, and even the knowledgeable creationist, but because it keeps popping up from time to time I thought I might explain (got nothing better to do---it's raining outside).
Fact of the matter is, monkeys still exist because we never replaced them. They evolved from early prosimians millions of years ago. Like 25 ++ millions of years ago, the same time another form of primate diverged from the prosimians, those that eventually evolved into the apes.
While recognizing that humans and monkeys were never that closely related---and we're not---some people think we humans evolved from apes, meaning the gorillas and orangutans, and question why these creatures are still around. Well, the answer is the same as that for the monkey question: Gorillas and orangutans still exist because we never replaced them; we evolved separately and in a different direction.
But, they will say, if that's true then why do evolutionists call humans "apes"? Easy answer: because of convention. When the ape lineages and the monkey lineages diverged the ape lineage became quite diverse,eventually embracing the gorillas, chimps, humans, etc. To denote this varied clad (group) of animals and so as to distinguish them from all the other primates, zoologists decided to call it the "ape" group. ("Ape" is thought to have come from the ability of these animals to mimic human expressions.) So, under the designation of "ape" we have the gorillas, orangutans, chimps, bonobos, gibbons, and humans.
Don't like being thought of as an ape? Tough!
Here's a graphic I put together to better visualize the relationships I'm talking about.