As you'd probably expect, this gets harder the further back you go. Firstly, even animals belonging to familiar groups are getting further away from their present-day forms. There comes a point where whales still walked on land, for instance. Secondly, the further we go back, the more animals we find that didn't leave any modern descendants, and, indeed, weren't even closely related to anything that did (Smilodon, for instance, has no living descendants, but it's still pretty obviously a cat). That can sometimes make it harder to say where such animals fit into the mammalian family tree or, perhaps more importantly, how they lived and behaved.
One such group of animals are the plesiadapoids, a category that includes at least three related "families" of tree-climbing mammal. These lived very early on, appearing in the earlier part of the first post-dinosaurian epoch, the Palaeocene, and dying out early on in the second one. They were relatively small, cat-sized, animals with slender bodies and long limbs and were common enough through Europe and North America that their remains are often used to help date some of the early deposits in those regions.
It has been known for a long time, based partly on the shape of their molar teeth, that plesiadapoids are in some way related to primates. But exactly how is less clear, and remains a bone of contention even today. Early theories suggested that they literally were primates, perhaps related to tarsiers, or at least to lemurs, somewhere in the outer reaches of the primate order (from the human perspective) but nonetheless part of it.
That no longer seems to be a common belief, with the plesiadapoids instead regarded forming their own group that branched off before the last common ancestor of all living primates lived. Nonetheless, while they are too specialised to be the likely ancestors of modern primates, many analyses conclude that they were at least more closely related to primates than to anything else alive today. Having said which, others have instead regarded them as closer to colugos (these are sometimes called "flying lemurs" although they aren't really lemurs, or even primates), or as forming a third group from which the ancestors of both primates and colugos diverged.
Since these are relatively small animals and lived a very long time ago, by mammal standards, the fossils we have of them are not very complete. This makes it difficult to say too much about them, but the little we can tell shows that, beyond climbing trees, they may not have been much like most modern primates. For instance, they had relatively small brains, the shape of which suggests that they relied heavily on the sense of smell, whereas living primates, including humans, are much more visually focussed.
There are other oddities about them, and while the best-known plesiadapoid is the type genus, Plesiadapis, arguably the strangest is Chiromyoides. This was originally named for a fossil discovered in France in 1916, with various other European specimens being discovered over the following decades. In 1973, the first North American example was discovered, and at least six different species native to the continent have since been named. (As always, given the fragmentary remains, it's possible that not all of these are really distinct... but equally, there may be more than we realise). These have been found in the western US from Texas to Montana and date from between 59 and 55 million years ago - which is to say, roughly where the end of the Paleocene passes into the beginning of the Eocene.
Most of these fossils are, it has to be said, fairly unimpressive. Most consist solely of teeth, although there are a few bits of jaw here and there. On the other hand, the teeth are what's strange about it, with most of the rest of what we'd guess about the animal being by analogy with its close relative Plesiadapis, of which we have rather more complete skeletons.
Specifically, the molars and premolars are unusually small, but the incisor teeth at the front of the mouth are remarkably large and bulky, while the lower jaw is short and heavily-built. This rather unusual arrangement suggests an equally unusual diet, at least for a primate-like animal. This is further supported by the fact that, while plesiadapoids in general are quite common, Chiromyoides seems to be rare where it is found, suggesting that whatever it did required a degree of specialisation, although not enough to stop it spreading widely.
Specimens from all the putative six North American species of Chiromyoides were recently re-examined in an effort to try and resolve some of the mystery and put this unusual animal into context. In terms of how it relates to other plesiadapoids, the new study doesn't really clarify the picture much, although it does at least seem to confirm that yes, this is a real genus and its closest relative probably is Plesiadapis. While they were at it, they identified a new species, C. kesiwah, from fossils found in Wyoming. (The second half of the scientific name is from the Shoshoni language, and means something like "rips with teeth").
However, how the different species within the genus relate to one another does seem to tell us something about the evolutionary history of the animal. The relative dates of the fossils, and which ones represent the most closely related species seems to indicate that it first appeared in what is now the southern US (Texas, perhaps) and then migrated northwards. Then some of those animals migrated eastward, crossing over into Europe via one of the early North Atlantic land bridges, where they may have survived for slightly longer than their American ancestors.
But what about those unusual teeth? A couple of previous proposals had been made as to what the animal would have used these for, with one possibility being that it fed on relatively hard seeds, which it needed to crack open. The new study, however, instead comes down in favour of the alternative proposal: that Chiromyoides was a "mammalian woodpecker".
By this they mean that, like woodpeckers, it fed on insects that bore beneath the wood of trees. In its case, rather than repeatedly whacking its head against a tree, it would have used the huge chisel-like incisors to rip open the bark before feeding. The authors point to a number of features of the skull that support this idea, including the shape and position of muscle attachments and a skull that seems well-suited to resisting the twisting force that would be applied against it.
This might seem a strange thing for a mammal to do, and in some respects it is. But there are a couple of points in its favour. For one, woodpeckers didn't exist at the time, it being around 30 million years too early, so they wouldn't have had direct competition. Secondly, there are mammals that live like this today, even if there's not very many of them.
These are the trioks and striped possums of New Guinea and tropical northeast Australia and, perhaps more famously, that utterly weird Madagascan primate the aye-aye (Daubentonia madagascariensis). A key feature that all of these living animals possess - although it's most noticeable in the aye-aye - is an elongated finger for winkling out grubs from the holes they bore in the wood. We don't have any foot bones for Chiromyoides, so we have no idea whether it had this feature or not and this would likely prove key to settling the question.
Living like a woodpecker does have some associated problems if you are not, in fact, an actual woodpecker. Aye-ayes, for example, take a long time to grow their front teeth (and Chiromyoides seems to have been the same, judging from what appears to be the jaw of a juvenile) which means that parents need to devote a lot of time to raising their young before they're ready to forage for themselves. It's a limited diet, even if it all it requires are the presence of trees with wood-boring insects, which would explain why the fossils in question are rare.
But we know that it's possible, and similar suggestions have been made for the fossil marsupial Yalkaparidon... so it might not even have been unique.
[Drawing by "Nobu Tamura", from Wikimedia Commons.]