If we came from monkeys, why are there still monkeys?

This is a broad question about how species arise.  It's sometimes answered by saying that we didn't come from the monkeys we see around us today, but we and monkeys came from a common ancestor.  This doesn't seem that helpful an answer to me, as it can't be denied that the common ancestor of humans and monkeys was more monkey-like than human-like.

One way to look at this question of speciation that might help is to think about territory. Imagine monkeys living in a large area of forest.  The forest does not go on forever, and the edge of the forest is likely to be a rather different environment than the broad area of the forest.  Then there is beyond the forest, which might be grassland.  The point is that some members of the monkey species will come across new environments, and there might be some members of those species which are more suited to those new environments, perhaps with longer (or shorter) limbs, for example.

Species can arise not because there is some constant pressure to diverge from a common ancestor, but simply because populations grown and environments aren't constant and infinite.

(Post asked for by @futbol91 on Twitter)