an omomyid from Wyoming
The primates are one of the larger groups of mammals, with literally hundreds of living species known. Naturally, there is a great deal of diversity across the primates but, at the highest level, we can divide them into two main suborders. These used to be referred to as the "lower" and "higher" primates, but that's misleading because the so-called lower primates have been evolving for just as long as the higher ones. It isn't as if they gave up one day and stopped evolving towards some ultimate goal of becoming human.
So, instead, when we aren't using the technical terms strepsirrhine and haplorrhine, today we tend to call them "wet-nosed" and "dry-nosed" primates, based on whether their nose is moist like that of a dog or not. When most people think of primates, however, it's likely the haplorrhine, or "dry-nosed" primates that they think of first, since this is the group that includes all the monkeys and apes - as opposed to lemurs and the like.