This is a question frequently posed by creationists—and quite often by perfectly rational people. It betrays a common misunderstanding of how evolution occurs. In this particular case, the answer also depends on what the questioner means by ‘monkeys’.
Human beings did not evolve from modern-day monkeys; human beings and modern-day monkeys both evolved from an extinct common ancestor (which was also, colloquially speaking, ‘a monkey’).
In the huge evolutionary family-tree of all the species that have ever lived on earth, humans and modern-day monkeys are close, living cousins.
The following analogy might help:
My father’s father died many years ago, but he left quite a few living descendants, including me, my sister, and my paternal cousins. To ask the question ‘If humans evolved from monkeys, how come there are still monkeys?’ is a bit like asking me ‘If you are descended from your grandfather, how come your cousins are still alive?’ The question doesn’t make any sense: why shouldn’t my cousins still be alive?
How new species evolve
As I said, asking the question ‘If humans evolved from monkeys, how come there are still monkeys?’ betrays a common misunderstanding of how new species evolve. The question seems to assume any new species must always replace its parent species. Presumably, the questioner is under the misapprehension either that: (a) parent species always evolve in their entirety into descendent species; or (b) descendent species always out-compete their parent species, driving them to extinction. Neither of these assumptions is correct. If they were correct, the total number of species on the planet would never increase, and the ‘family tree’ of species would not be a tree at all, but a vast collection of entirely separate lines (or ladders) of descent. In reality, parent species can spawn several child species, thereby initiating an entire ‘family tree’ of descendent species.
New species usually arise when a relatively small sub-population of an existing species becomes isolated from the rest of the species in some way, and diverges genetically from the parent population.
Circumstances will differ from case to case, but the main cause for this genetic divergence will usually be the two populations’ continuing to adapt to their different environments through Darwinian Natural Selection. But even if the selective pressures in the two environments are very similar, the fact that the two populations are isolated from each other means some genetic divergence is bound to occur. Random changes in the genetic make-up of the two different populations mean they will drift further and further apart over the generations.
If the two populations continue to diverge, and remain isolated long enough to prevent inter-breeding, they will eventually become so different from each other that they can no longer be considered to be the same species. Separation leads to divergence leads to speciation.
So did we evolve from monkeys or not?
As I said at the beginning, it depends on what you mean by ‘monkeys’.
Modern-day ‘monkeys’ comprise two distinct groups: the Old World monkeys (living in Africa, Asia and Gibraltar), and the New World monkeys (living in Central and South America). These ‘monkeys’ form part of the simian family tree, which also includes modern-day apes and us humans.
Around 40 million years ago, a new sub-population branched out from the simian family tree. A small sub-population of this new branch—a twig, if you will—eventually crossed the (much narrower in those days) Atlantic and evolved into the modern-day New World monkeys. The rest of their branch remained in the Old World and eventually became extinct.
The main section of the simian family tree, from which the New World monkeys’ section had branched out, branched again around 25 million years ago. One branch eventually evolved into the modern-day Old World monkeys, the other into the apes (and, eventually, us humans).
Perhaps a simple (bordering on simplistic) diagram might help:
Somewhat counter-intuitively, therefore, humans and Old World monkeys have a more recent common ancestor (i.e. they are more closely related to each other) than Old World and New World monkeys. This, perhaps surprising, conclusion is backed up by masses of morphological and genetic evidence. For example, humans and Old World monkeys have the same number of teeth; New World monkeys have an extra set of premolars.
So, how do you define a monkey?
You could quite reasonably argue that, if modern-day Old World Monkeys are ’monkeys’, and modern-day New World monkeys are ‘monkeys’, then it stands to reason any species descended from their most recent common ancestor must also be ‘a monkey’. But, as we have seen, that includes us. In which case, not only did we humans evolve from monkeys, but we still are monkeys!
But you might equally reasonably choose to exclude humans (and apes) from your definition of monkeys. In which case, the colloquial word ‘monkey’ (as used to refer to both modern-day Old World and modern-day New World monkeys, but not humans or apes) becomes scientifically meaningless. In which case, the original question is also meaningless, as, scientifically speaking, there is no such thing as ‘a monkey’!