Although the risk is low, volcanologists continue to monitor the Yellowstone caldera for signs that an eruption might be imminent. That's because the scale of such an eruption would be unprecedented in human history. Phys.org has published an article that describes the effects that such an eruption would have. It wouldn't be pleasant.
Despite the scale, no known human witnessed the cataclysm. As far as we know, early humans had not yet reached the continent. Across oceans, perhaps early humans wondered at the hazier skies and unusually vivid sunsets. Volcanic particles circulating in the sky cooled their climate and likely affected their weather patterns and lives. Whether they noted these changes—or connected them to any distant event—is unknowable.
Today, humanity would certainly notice. We already know that a super-eruption on this scale would threaten civilization as we know it. So what exactly would we experience if Yellowstone erupted? We are experts in disasters and volcanoes, and what follows is a thought experiment into what might happen in the worst-case scenario. We've based our hypothesis on research and an examination of how countries have dealt with disasters in recent years.
If you want a fictional portrayal, check out Harry Turtledove's Supervolcano trilogy (Eruption, All Fall Down, Things Fall Apart). I read this a few years ago and it' matches the phys.org article quite closely.
