I've seen the idea that there are no primates adapted to eating grains, but actually there is a primate that is better adapted to such a diet than any others. It's the gelada (Theropithecus gelada), which lives only in the Ethopian highland grasslands. The gelada is the only living member of genus the Theropithecus. Several larger gelada species once roamed most of Africa, including the terrifying giant gelada, which was around the size of a modern gorilla. But now there is just one, which is also one of the few primates that endures sub-freezing temperatures, which occur at night in the highlands.
The gelada is also quite interesting because it is a grazer, relying mainly on grass. It prefers the seeds of the grass, which are yes, grains.
This is unusual for primates. Some, like anthropologist Clifford Jolly, have speculated that hominids once occupied a similar niche. But this was mostly in the 1970s and this model for understanding human origins has fallen out of favor. Some extinct lines on the family tree (Paranthropus for example) were thought to have eaten similar diets based on low-quality plants, but more recent evidence has cast doubt on this theory. Frederick Szalay's reply to Jolly's paper in 1975 noted that as climate changed, hominids and the ancestors of gelada may have both moved into the grasslands.
But as hominids rose, the Theropithecus genus fell, backed into a corner by adapatations to eating grass that seem incomplete and inefficient. Geladas require very high quality grass, not the low quality grass that started to dominate as Africa warmed up again.
The gelada and related baboon line seems to have a longer history of consuming starchier foods than the frugivorous lines that led to us. One piece of evidence is that baboons and geladas have higher salivary amylase expression than even humans cultures adapted to high starch diets.
Unfortunately, it seems that particular this genus adapted itself into a corner, with adaptations not good enough to compete with animals like zebras for the increasingly low-quality grasses in the warmer low-altitude grasslands, but complete enough that grass-eating was probably obligatory. Primates with an ability to consume a more flexible diet, like our ancestors, rose, while most Theropithecus died out.
Why such big scary teeth on a grass eater? Big scary teeth are about more than food, they are also the hallmark of territorial species where males fight for domination of harems of females as seen in this video of a gelada male battle.
While geladas were busy chomping on grass pretty much all day, there is some good evidence our ancestors were scavenging large animal carcasses, developing a taste for meat and perhaps spurring us to eventually hunt and develop tools to acquire more protein this way. The geladas went the route of low-quality protein, while the hominids went the route of high-quality protein, protein that may have allowed us to develop large brains and free up time from foraging to develop advanced culture. Geladas probably got less intelligent due to their overspecialization, while hominids and their closely related baboon cousins used their intelligence and flexibility to thrive in a variety of habitats.
Later, our niches would cross again as humans developed our own way to extract energy more efficiently from grass through technology and selective breeding for grain yields. Not surprisingly, geladas are thrilled to munch on such high quality grasses. While they are not a big as their ancestors, they are still a formidable pest ,as this Human Planet video shows:
Researching geladas might give us valuable clues to understanding our own species. For example, looking at the adaptations geladas have to eating their diet could tell us something about the kind of challenges a grain-eating primate faces and we could compare them to our own physiology to see how well we have adapted or not adapted to similar dietary challenges. However, geladas eat wild uncooked grasses, whereas humans have an entire culture of complex preparation that alters the structure and composition of our food significantly through grinding, fermenting, cooking, and other technology.