The primates are one of the major groups within placental mammals, currently considered to contain at least fourteen different living 'families', and probably more. Given this, and the fact that they are fairly distinctive, it's not surprising to discover that they are also a very ancient group. Genetic studies, back by estimates of how frequently mutations ought to occur, imply that they may date all the way back to the extinction of the dinosaurs, or at least its immediate aftermath.
The oldest undisputed fossil primate we currently know of isn't quite that old, however, and dates back 'only' 55 million years to the dawn of the Eocene epoch. I have to add the word 'undisputed' to that, though, because it wasn't alone - a number of other very primate-like animals did live at the same time, and, indeed, somewhat earlier.
These animals are collectively called 'plesiadapiforms', and it would be fair to say that there is still some considerable debate as to what they actually were. Just as with the question as to how many families of living primate there are, this depends not on how the different groups are related, but on where we choose to draw the lines between them. In the case of living families, the question is whether we consider
marmosets and night monkeys to belong to the broader capuchin family, or whether we consider them different enough to count as families in their own right. In the case of the plesiadapiforms, it's whether they're really weird
early primates, or whether we consider them to be merely close relatives.