Two thousand years ago the ancient Romans had some imaginative solutions to the problem of what to do with statues of rulers they had come to deplore. Some they gleefully toppled and threw into the nearest river, Edward Colston-style. But others they carefully reworked. It didn’t take much to get out a chisel and refashion the face of the old tyrant into the face of the new beloved leader. If cash was very tight, you might just put a new name on to an old statue, because hundreds of miles away hardly anyone knew what these guys really looked like. As Alex von Tunzelmann deftly captures in her recent book, Fallen Idols, statues are always works in progress: toppled, moved, reworked, reerected and reinterpreted. There has never been a time when they were not contested. Centuries later, images of Roman emperors are still part of the backdrop of power. There is hardly a stately home or a modern museum in the west that does not have its line-up of busts of the first “12 Caesars”, from Julius Caesar (assassinated 44BC) to Domitian (assassinated AD96). These are sometimes authentic ancient portraits, but more often they are slightly over-the-top replicas created in the 17th or 18th centuries. Most of us, me included, walk straight past them, as if they were merely the predictable backdrop to the power politics of the past, designed to give a hint of the allure of “the Caesars” to each new man on the make. They are not much more than pricey wallpaper. Sometimes they are exactly that. In fact, some of the earliest European wallpaper to survive features the heads of Roman emperors. But it doesn’t take much thought to see the problem here: they are hardly figures to be admired. They have gone down in history as an unsavoury bunch, almost universally derided, and of the famous first 12, Julius Caesar to Domitian, there was only one (the down-to-earth Vespasian who came to the throne in AD69) for whom there was no suggestion that he had been murdered or forced to take his own life. So what were they doing centuries later plastered over the palaces of dynasts? And does this have anything to teach us in our own “culture wars”? Does it help us think a bit harder about what images of power, and the powerful, are for? My favourite example is the decoration of the so-called King’s Staircase at Hampton Court Palace – painted in the early 18th century, decades after the palace’s Tudor heyday, by Antonio Verrio. An exercise in “extreme baroque”, it is now usually ignored by visitors, if not deplored: “gaudy colour, bad drawing and senseless composition” as one unimpressed 19th-century critic dubbed it. But it is, in fact, far from “senseless”. It is a clever illustration of a niche satirical skit written by the emperor Julian in the fourth century AD about his predecessors. In this squib Julian imagines that a group of those earlier rulers, now long dead, were keen to have dinner with the Roman gods, but that the gods were not so sure – and after much to-ing and fro-ing, and a good bit of character assassination, withdrew the invitation. What we see in the painting is a colourful lineup of emperors, including a rather haughty Julius Caesar and a dissolute Nero. They have not yet been told that they will not be dining with the gods at the empty table that is balanced in the clouds above their heads. But they soon will be. What on earth is this scene doing on the main staircase up to the king’s apartments? What was the king – or his visitors, or his servants – to make of this parade of classical rulers, almost all of whom fell somewhere on the spectrum between villain and idiot? There have been many modern attempts to explain it. Was there a coded religious message here, in the conflicts between Roman Catholics and Protestants? Or were most people in the 18th century as uncertain about the story behind the painting as we are? (Julian’s skit was a bit better known then but, honestly, not much.) None of these ideas quite get around the problem of the glaring mismatch between the ancient figures on such prominent display and the public relations of the 18th-century monarch. And significantly it is a mismatch found elsewhere at Hampton Court. A much more admired set of paintings in the palace are Andrea Mantegna’s The Triumphs of Caesar, painted in the 15th century and brought to England in Charles I’s great haul of artworks from Mantua, Italy, in the early 17th century. It is a glorious series of images, recreating the lavish Roman processions held to celebrate Julius Caesar’s military victories. In the final canvas we see a rather gaunt Caesar himself carried along in his triumphal chariot. You did not have to know very much about Caesar’s career to know that the next big event was his own assassination. Oliver Cromwell, I suspect, got the point. These paintings were among the few of the king’s portable artworks Cromwell did not sell off. This royal palace, in other words, was decorated with images that did not simply use the past to bolster the power of the modern monarchy, but set up all kinds of questions and debates about the nature of autocracy, and how it should be judged; and it exposed to the monarch himself, at the heart of his palace, the awkward underbelly of one-man rule, and its sometimes nasty end. There is a message here for us, too, in thinking about the statues in our own public spaces. Certainly, many of these were put up to celebrate those we no longer wish to celebrate. And I doubt there is anyone who thinks there are some that are not better toppled. But we miss part of the point if we think the only long-term function of these works of art is celebratory, whatever the motivations were for putting them up in the first place. The statues now have an important job to do in helping us face up to the past, in focusing our justifiable anger, or at least ambivalence, about some of those we were taught to regard as “heroes”, and in prompting us to ask how much “better” than them we really are, or should be. To put it another way, when I look at that bronze statue of Charles I on horseback that now stands just off Trafalgar Square in London, I do not see him as a hero to be worshipped or as a martyr to be venerated; nor do I feel the slightest twinge of regret for the “divine right of kings”, or any of the other dreadful ideas for which he stood. I see him as a useful reminder of the costs we sometimes have to pay for progress (in this case, his execution), and as an affirmation that we really have done better since then. He has not yet, so far as I know, been marked out for the chop a second time around. Mary Beard is a professor of classics at Cambridge University. Her new book Twelve Caesars: Images of Power from the Ancient World to the Modern is out today Mary Beard and the Guardian’s Charlotte Higgins will discuss the enduring appeal of the Greek myths at a Guardian Live online event on 3 November. Book tickets here